The first eigenvalue of Laplace-type elliptic operators induced by conjugate connections
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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.
Mathematics Subject Classification
53C24 53C40 35P15 53A15Keywords
Conjugate connections Laplace-type operator first eigenvalue characterization of hyperellipsoidsPreview
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