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Register a new userGeneral Schwarz Lemmata and their applications
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Authors
Lei Ni
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We prove estimates interpolating the Schwarz Lemmata of Royden-Yau and the ones recently established by the author. These more flexible estimates provide additional information on (algebraic) geometric aspects of compact Kahler manifolds with nonnegative holomorphic sectional curvature, nonnegative $Ric_ell$ or positive $S_ell$.
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The notion of different kind of algebraic Casorati curvatures are introduced. Some results expressing basic Casorati inequalities for algebraic Casorati curvatures are presented. Equality cases are also discussed. As a simple application, basic Casorati inequalities for different $delta $-Casorati curvatures for Riemannian submanifolds are presented. Further applying these results, Casorati inequalities for Riemannian submanifolds of real space forms are obtained. Finally, some problems are presented for further studies.
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