zero-dimensional. Bochner's theorem then follows from the fact that the isometry group of a closed Riemannian manifold is compact. Bochner's result on Killing...

Riemannian geometry is the branch of differential geometry that studies Riemannian manifolds, defined as smooth manifolds with a Riemannian metric (an...

Two theorems in the mathematical field of Riemannian geometry bear the name Myers–Steenrod theorem, both from a 1939 paper by Myers and Steenrod. The first...

the mathematical field of differential geometry, there are various splitting theorems on when a pseudo-Riemannian manifold can be given as a metric product...

In mathematics, Bochner's formula is a statement relating harmonic functions on a Riemannian manifold ( M , g ) {\displaystyle (M,g)} to the Ricci curvature...

However, it is a precise theorem of differential geometry and geometric analysis, in which physical systems are modeled by Riemannian manifolds with nonnegativity...

(differential geometry) Soul theorem (Riemannian geometry) Sphere theorem (Riemannian geometry) Synge's theorem (Riemannian geometry) Toponogov's theorem (Riemannian...

differential geometry, the Ricci curvature tensor, named after Gregorio Ricci-Curbastro, is a geometric object which is determined by a choice of Riemannian or...

Laplacian comparison theorem in Riemannian geometry, which relates the Laplace–Beltrami operator, as applied to the Riemannian distance function, to...

rather than Riemannian manifolds, would have a number of significant applications, with analogues of the classical Eells−Sampson rigidity theorem giving novel...

give a probabilistic proof of the Atiyah-Singer index theorem. Stochastic differential geometry also applies in other areas of mathematics (e.g. mathematical...

works on nonlinear partial differential equations in Lorentzian and Riemannian geometry and their applications to general relativity and topology." In 2024...

(graph theory) Cheeger–Müller theorem soul theorem splitting theorem Collapsing manifold L² cohomology Riemannian geometry Faculty Profile 1984 U.S. and...

1993) was a mathematician working on differential geometry who introduced the Bochner–Yano theorem. He also published a classical book about geometric...

In the mathematical field of differential geometry, a smooth map between Riemannian manifolds is called harmonic if its coordinate representatives satisfy...

number Complex geometry CR manifold Dolbeault cohomology Harmonic maps Harmonic morphisms Infinite-dimensional holomorphy Oka–Weil theorem That is an open...

vanishing theorem Kodaira–Spencer mapping Kodaira dimension Kodaira surface Kodaira embedding theorem Kodaira's classification of singular fibers Bochner–Kodaira–Nakano...

calculus of variations. Generalizing Bochner's work on harmonic functions, Eells and Sampson derived the Bochner identity, and used it to prove the triviality...

computer scientist Hisashi Kobayashi. His research interests were in Riemannian and complex manifolds, transformation groups of geometric structures,...

This optimal result is known as the sphere theorem for Riemannian manifolds. The Rauch comparison theorem is also named after Harry Rauch. He proved it...

the geometry and analysis on symmetric spaces. In particular, he used new integral geometric methods to establish fundamental existence theorems for differential...

Riemannian structure (R) of X {\displaystyle X} . The construction of these operators is standard in the literature on complex differential geometry....

Salomon Bochner for his cumulative influence on the fields of probability theory, Fourier analysis, several complex variables, and differential geometry. 1979...

variables. 1925 Luther P. Eisenhart (Princeton University): Non-Riemannian geometry. 1925 Dunham Jackson (University of Minnesota): The Theory of Approximations...

theory of special functions, and to the theory of Riemannian symmetric spaces in differential geometry. Broadly speaking, the theory exists to abstract...