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12 relations: Bochner identity, Gradient, Graduate Studies in Mathematics, Harmonic function, Laplace–Beltrami operator, Mathematician, Mathematics, Ricci curvature, Riemannian manifold, Salomon Bochner, United States, Weitzenböck identity.
Bochner identity
In mathematics — specifically, differential geometry — the Bochner identity is an identity concerning harmonic maps between Riemannian manifolds.
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Gradient
In mathematics, the gradient is a multi-variable generalization of the derivative.
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Graduate Studies in Mathematics
Graduate Studies in Mathematics (GSM) is a series of graduate-level textbooks in mathematics published by the American Mathematical Society (AMS).
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Harmonic function
In mathematics, mathematical physics and the theory of stochastic processes, a harmonic function is a twice continuously differentiable function f: U → R where U is an open subset of Rn that satisfies Laplace's equation, i.e. everywhere on U. This is usually written as or.
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Laplace–Beltrami operator
In differential geometry, the Laplace operator, named after Pierre-Simon Laplace, can be generalized to operate on functions defined on surfaces in Euclidean space and, more generally, on Riemannian and pseudo-Riemannian manifolds.
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Mathematician
A mathematician is someone who uses an extensive knowledge of mathematics in his or her work, typically to solve mathematical problems.
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Mathematics
Mathematics (from Greek μάθημα máthēma, "knowledge, study, learning") is the study of such topics as quantity, structure, space, and change.
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Ricci curvature
In differential geometry, the Ricci curvature tensor, named after Gregorio Ricci-Curbastro, represents the amount by which the volume of a small wedge of a geodesic ball in a curved Riemannian manifold deviates from that of the standard ball in Euclidean space.
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Riemannian manifold
In differential geometry, a (smooth) Riemannian manifold or (smooth) Riemannian space (M,g) is a real, smooth manifold M equipped with an inner product g_p on the tangent space T_pM at each point p that varies smoothly from point to point in the sense that if X and Y are differentiable vector fields on M, then p \mapsto g_p(X(p),Y(p)) is a smooth function.
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Salomon Bochner
Salomon Bochner (20 August 1899 – 2 May 1982) was an American mathematician, known for work in mathematical analysis, probability theory and differential geometry.
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United States
The United States of America (USA), commonly known as the United States (U.S.) or America, is a federal republic composed of 50 states, a federal district, five major self-governing territories, and various possessions.
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Weitzenböck identity
In mathematics, in particular in differential geometry, mathematical physics, and representation theory a Weitzenböck identity, named after Roland Weitzenböck, expresses a relationship between two second-order elliptic operators on a manifold with the same leading symbol.
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