Robert Hermann
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American mathematician
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Robert Hermann mathematics Degrees
Mathematics
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Mathematics
Robert Hermann 's Degrees
- PhD Mathematics University of California, Berkeley
- Masters Mathematics University of California, Berkeley
- Bachelors Mathematics University of California, Berkeley
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Why Is Robert Hermann Influential?
(Suggest an Edit or Addition)According to Wikipedia, Robert C. Hermann was an American mathematician and mathematical physicist. In the 1960s Hermann worked on elementary particle physics and quantum field theory, and published books which revealed the interconnections between vector bundles on Riemannian manifolds and gauge theory in physics, before these interconnections became "common knowledge" among physicists in the 1970s.
Robert Hermann 's Published Works
Number of citations in a given year to any of this author's works
Total number of citations to an author for the works they published in a given year. This highlights publication of the most important work(s) by the author
Published Works
- Lie Groups, Lie Algebras, and Some of Their Applications (1974) (1487)
- Differential geometry and the calculus of variations (1970) (285)
- Geometry, physics, and systems (1973) (208)
- A sufficient condition that a mapping of Riemannian manifolds be a fibre bundle (1960) (168)
- Lie Groups for Physicists (1967) (167)
- On the Accessibility Problem in Control Theory (1963) (158)
- Applications of Algebraic Geometry to Systems Theory: The McMillan Degree and Kronecker Indices of Transfer Functions as Topological and Holomorphic System Invariants (1978) (132)
- Applications of algebraic geometry to systems theory--Part I (1977) (120)
- Sophus Lie's 1880 transformation group paper (1975) (98)
- Vector bundles in mathematical physics (1970) (90)
- Review: L. V. Ovsiannikov, Group analysis of differential equations (1983) (80)
- Pseudopotentials of Estabrook and Wahlquist, the Geometry of Solitons, and the Theory of Connections (1976) (72)
- E. Cartan's geometric theory of partial differential equations (1965) (67)
- Development of mathematics in the 19th century (1979) (63)
- Geometry of Riemannian spaces (1983) (58)
- The formal linearization of a semisimple Lie algebra of vector fields (1968) (58)
- Variational completeness for compact symmetric spaces (1960) (53)
- Review: A. O. Barut, Electrodynamics and classical theory of fields and particles (1964) (52)
- Symplectic geometry and Fourier analysis (1977) (48)
- Gauge fields and Cartan-Ehresmann connections (1975) (47)
- Sophus Lie's 1884 differential invariant paper (1975) (44)
- On the Differential Geometry of Foliations (1960) (41)
- Lectures in mathematical physics (1970) (40)
- Review: Jeff Cheeger and David G. Ebin, Comparison theorems in Riemannian geometry (1976) (38)
- Some differential-geometric aspects of the Lagrange variational problem (1962) (32)
- Lie algebras and quantum mechanics (1970) (32)
- Analytic continuation of group representations (1966) (32)
- Hilbert's invariant theory papers (1978) (30)
- Yang-Mills, Kaluza-Klein, and the Einstein Program (1978) (28)
- Totally Geodesic Orbits of Groups of Isometries (1962) (27)
- Geodesics of singular Riemannian metrics (1973) (26)
- Group Representations in Mathematics and Physics (1970) (23)
- Fourier analysis on groups and partial wave analysis (1969) (23)
- Focal points of closed submanifolds of riemannian spaces (1963) (23)
- The geometry of non-linear differential equations, Bäcklund transformations, and solitons (1976) (22)
- Quantum Statistical Mechanics and Lie Group Harmonic Analysis (1980) (20)
- Secondary obstructions for fibre spaces (1959) (20)
- Cartanian Geometry, Nonlinear Waves, and Control Theory (1970) (19)
- Geometric aspects of potential theory in the bounded symmetric domains (1962) (18)
- The Gell-Mann formula for representations of semisimple groups (1966) (17)
- Spinors, Clifford, and Cayley algebras (1974) (17)
- Inverse Scattering Technique of Soliton Theory, Lie Algebras, the Quantum Mechanical Poisson-Moyal Bracket, and the Rotating Rigid Body (1976) (17)
- The Second Variation for Minimal Submanifolds (1966) (17)
- Energy Momentum Tensors (1973) (16)
- Compact homogeneous almost complex spaces of positive characteristic (1956) (16)
- Applications of algebraic geometry to systems theory, part II: Feedback and pole placement for linear Hamiltonian systems (1977) (15)
- Linear systems and the differential field of Heaviside operators (1981) (15)
- Topics in the Mathematics of Quantum Mechanics (1973) (15)
- Differential form methods in the theory of variational systems and Lagrangian field theories (1988) (14)
- Geometric aspects of potential theory in the symmetric bounded domains, II (1963) (14)
- Toda lattices, cosymplectic manifolds, Bäcklund transformations, and kinks (1977) (14)
- Lie and morse theory for periodic orbits of vector fields and matrix riccati equations, I: General lie-theoretic methods (1981) (13)
- Existence in the large of totally geodesic submanifolds of Riemannian spaces (1960) (13)
- Geodesics and Classical Mechanics on Lie Groups (1972) (13)
- Infinite dimensional Lie algebras and current algebra (1970) (12)
- ON THE EXISTENCE OF A FUNDAMENTAL DOMAIN FOR RIEMANNIAN TRANSFORMATION GROUPS (1962) (11)
- Differential Geometry, Lie Groups, and Symmetric Spaces (Sigurdur Helgason) (1980) (11)
- Spectrum Generating Algebras and Symmetries in Mechanics. I (1972) (11)
- Ricci and Levi-Civita's tensor analysis paper (1975) (11)
- Quantum and fermion differential geometry (1977) (11)
- Lie and Morse theory for periodic orbits of vector fields and matrix Riccati equations, II (1983) (10)
- Invariants for feedback equivalence and Cauchy characteristic multifoliations of nonlinear control systems (1988) (10)
- Infeld–Hull factorization, Galois–Picard–Vessiot theory for differential operators (1981) (10)
- Obstruction theory for fibre spaces (1960) (10)
- The differential geometric structure of general mechanical systems from the Lagrangian point of view (1982) (10)
- Periodic solutions of the Riccati equation (1980) (10)
- Homogeneous riemannian manifolds of non-positive sectional curvature (1963) (10)
- Algebro-geometric and Lie-theoretic techniques in systems theory (1977) (9)
- Current Algebras, the Sugawara Model, and Differential Geometry (1970) (9)
- Some remarks on the geometry of systems (1973) (9)
- Geometric structure theory of systems-control, theory and physics (1974) (9)
- C-O-R Generalized Functions, Current Algebras, and Control (1995) (9)
- The theory of equivalence of Pfaffian systems and input systems under feedback (1981) (9)
- Lie theoretic aspects of the Riccati equation (1977) (8)
- Remarks on the Geometric Nature of Quantum Phase Space (1965) (8)
- Topics in General Relativity (1977) (8)
- The second variation for variational problems in canonical form (1965) (8)
- Geometric structure of systems-control theory and physics (1976) (8)
- Geometric Formula for Current-Algebra Commutation Relations (1969) (8)
- Linear systems theory and introductory algebraic geometry (1974) (8)
- Physical Aspects of Lie Group Theory (1975) (7)
- Formal linearization of vector fields and related cohomology. II (1973) (7)
- Geometric aspects of potential theory in symmetric spaces. III (1964) (7)
- Analytic continuation of group representations. IV (1967) (6)
- A POISSON KERNEL FOR CERTAIN HOMOGENEOUS SPACES (1961) (6)
- Equivalence invariants for submanifolds of homogeneous spaces (1965) (6)
- Geometric construction and properties of some families of solutions of nonlinear partial differential equations. I (1983) (6)
- Currents in Classical Field Theories (1972) (6)
- Topics in the Geometric Theory of Linear Systems (1984) (6)
- The geometric theory of deformation and linearization of Pfaffian systems and its applications to system theory and mathematical physics. I (1983) (6)
- QUANTUM FIELD THEORIES WITH DEGENERATE LAGRANGIANS. (1969) (6)
- On geodesics that are also orbits (1960) (6)
- Existence in the large of parallelism homomorphisms (1963) (5)
- Prolongations, Bäcklund Transformations, and Lie Theory as Algorithms for Solving and Understanding Nonlinear Differential Equations (1978) (5)
- Constrained mechanics and Lie theory (1992) (5)
- Applications of Algebraic Geometry to Systems Theory (2011) (5)
- Geodesics of bounded, symmetric domains (1961) (5)
- COMPACTIFICATIONS OF HOMOGENEOUS SPACES AND CONTRACTIONS OF LIE GROUPS. (1964) (5)
- Quantum mechanics and geometric analysis on manifolds (1982) (5)
- Review: Harley Flanders, Differential forms with applications to the physical sciences (1964) (4)
- ‘Modern’ differential geometry in elementary particle physics (1978) (4)
- GENERAL MASS FORMULA FOR THE NAMBU WAVE EQUATIONS. (1968) (4)
- Nonlinear feedback control and systems of partial differential equations (1989) (4)
- Mathematics and Bourbaki (1986) (4)
- Topics in Physical Geometry (1988) (4)
- Group representations and creation operators (1966) (4)
- General Algebraic Ideas (1973) (3)
- The geometric foundations of the integrability property of differential equations and physical systems. I. Lie’s ‘‘function groups’’ (1983) (3)
- Analytic continuation of group representations II (1966) (3)
- Topics in the Geometric Theory of Integrable Mechanical Systems (1985) (3)
- Representations of Groups, with Special Consideration for the needs of Modern Physics. (1965) (3)
- Review: S. Sternberg, Lectures on differential geometry (1965) (3)
- A Lie-theoretic setting for the classical interpolation theories (1986) (3)
- Pfaffian systems and feedback linearization/obstructions (1983) (3)
- Remarks on the Foundations of Integral Geometry (1960) (3)
- Analytic continuation of group representations. III (1966) (3)
- The 1976 Ames Research Center (NASA) Conference on the Geometric Theory of Non-linear Waves (1977) (3)
- Linear systems with structure group and their feedback invariants (1977) (2)
- A uniqueness theorem for minimal submanifolds (1968) (2)
- Algebraic and geometric structure of linear filters and scattering systems. I (1981) (2)
- A ‘geometric’ view of the dynamics of trajectories of computer programs (1990) (2)
- Perturbation theory for nonlinear feedback control systems and spencer-goldschmidt integrability of linear partial differential equations (1990) (2)
- Algebraic topics of importance in systems theory (1975) (2)
- Lax representation as a "quantization" of the function groups of Sophus Lie (1982) (2)
- Differential equations of the matrix elements of the degenerate series (1967) (2)
- Treatise on Analysis, Vol. IV (J. Dieudonné) (1977) (2)
- The geometric foundations of the integrability property of differential equations and physical systems. II. Mechanics on affinely‐connected manifolds and the work of Kowalewski and Painlevé (1984) (1)
- A view of applied mathematics (1978) (1)
- Geometric and Lie-Theoretic Principles in Pure and Applied Deformation Theory (1988) (1)
- Analytic continuation of group representations-V (1967) (1)
- Review: Shoshichi Kobayashi and Katsumi Nomizu, Foundations of differential geometry (1964) (1)
- BOHR-SOMMERFELD QUANTIZATION IN GENERAL RELATIVITY AND OTHER NONLINEAR FIELD AND PARTICLE THEORIES (1980) (1)
- Linear and tensor algebra (1973) (1)
- Analytic continuation of group representations. VI (1966) (1)
- An Analogue of M. Riesz's Mean Value Theorem in the Theory of Absolute Summability (1969) (1)
- ALGEBRAIC AND GEOMETRIC STRUCTURES IN CURRENT ALGEBRA THEORY. (1970) (1)
- C-W cell decompositions of symmetric homogeneous spaces (1960) (1)
- Global Lorentzian Geometry (John K. Beem and Paul E. Ehrlich) (1983) (1)
- Fiber Spaces, Connections and Yang-Mills Fields, (1982) (1)
- Time-varying linear systems and the theory of non-linear waves (1978) (1)
- Representations of groups containing the Poincaré group. I (1966) (1)
- Some algebraic, geometric, and system‐theoretic properties of the Special Functions of mathematical physics (1982) (1)
- Svstem Theory as Applied v lkkrential Geometry (2000) (0)
- Differential Forms in Mathematical Physics (C. Von Westenholz) (1980) (0)
- Geometric foundations of the theory of feedback equivalence (1987) (0)
- The Theory of Spinors. By Elie Cartan (1983) (0)
- Isomonodromy as a curvature‐zero condition (1981) (0)
- Book Review: Quantum physics, relativity and complex spacetime (1993) (0)
- Mathematicians and science. (1983) (0)
- Exterior Differential Systems and the Calculus of Variations. (Phillip A. Griffiths) (1984) (0)
- Compactification of Minkowski Space and SU(3) Symmetry (1965) (0)
- Deformation of Lie group representations and linear filters, Part I (1983) (0)
- lkkrential Geometry (2000) (0)
- Geometric Computing Science: First Steps (1991) (0)
- DISCRETE SYMMETRIES OF ELEMENTARY PARTICLE PHYSICS. (1967) (0)
- A grassmannian approach to scattering systems (1982) (0)
- A geometric variational formalism for the theory of nonlinear waves (1980) (0)
- Geometric Structures in Nonlinear Physics (1992) (0)
- Review: G. L. Lamb, Jr., Elements of soliton theory (1981) (0)
- Differential Geometric Methodology and Foundations for the Theory of Nonlinear Differential Equations. (1983) (0)
- Singular and Degenerate Cauchy Problems (R. W. Carroll and R. E. Showalter) (1978) (0)
- Lie-Cartan-Ehresmann Theory (1993) (0)
- The 1976 Ames Research Center (NASA) Conference on Geometric Control Theory : articles (1977) (0)
- Energy-momentum tensors and deformation of metrics (1973) (0)
- Physics and geometry (1980) (0)
- A brief survey of constrained mechanics and variational problems in terms of differential forms (1994) (0)
- Base decisions on traditions (1968) (0)
- Review: Louis Auslander and Robert E. MacKenzie, Introduction to differentiable manifolds (1964) (0)
- GEOMETRIC IDEAS IN LIE GROUP HARMONIC ANALYSIS THEORY. (1970) (0)
- Dynamical systems defined on infinite dimensional lie algebras of the ''current algebra'' or ''Kac-Moody'' type (1982) (0)
- System theory as applied differential geometry. [linear system (1979) (0)
- Lie-Theoretic Ode Numerical Analysis, Mechanics and Differential Systems (1994) (0)
- Geometric Structure and Moving Frames for the Generalized Toda Lattices (1980) (0)
- A new application of algebraic geometry to systems theory (1976) (0)
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