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- Title
The first eigenvalue of Laplace-type elliptic operators induced by conjugate connections.
- Authors
Simon, Udo
- Abstract
According to Tashiro-Obata, on a Riemannian manifold ( M, g) with its Ricci curvature bounded positively from below, the first eigenvalue of the Laplacian on functions satisfies a simple inequality in terms of the scalar curvature, and equality characterizes the Riemannian sphere. We discuss a similar inequality for a certain elliptic operator on a manifold with conjugate connections. As application we characterize hyperellipsoids in Blaschke's unimodular-affine hypersurface theory.
- Subjects
RIEMANNIAN manifolds; HYPOELLIPTIC operators; PARTIAL differential operators; DIFFERENTIAL geometry; MANIFOLDS (Mathematics)
- Publication
Journal of Geometry, 2015, Vol 106, Issue 2, p313
- ISSN
0047-2468
- Publication type
Article
- DOI
10.1007/s00022-014-0250-2