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Submanifolds with Restrictions on Q-Ricci Curvature

In: New Developments in Differential Geometry, Budapest 1996

Author

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  • V. Yu. Rovenskii

    (Pedagogical State University Lebedevoi, Geometry Chair)

Abstract

The role of q—Ricci curvature (intrinsic and extrinsic) in the theory of submanifolds is discussed. In Section 2 the estimate of the distance between two compact submanifolds in a space of positive q—Ricci curvature is given and its application to special classes of submanifolds is considered. In Section 3 we generalize a lemma of T. Otsuki on asymptotic vectors of a bilinear form and then prove a theorem of nonembedding into simply connected Riemannian spaces with nonpositive curvature. In Section 4 the estimate from below of the index of relative nullity of a sub-manifold with nonpositive extrinsic q—Ricci curvature is given. Corollaries are extremal theorems for compact submanifolds in a Riemannian space with positive curvature, in which totally geodesic submanifolds and space forms are characterized.

Suggested Citation

  • V. Yu. Rovenskii, 1999. "Submanifolds with Restrictions on Q-Ricci Curvature," Springer Books, in: J. Szenthe (ed.), New Developments in Differential Geometry, Budapest 1996, pages 375-388, Springer.
    • Handle: RePEc:spr:sprchp:978-94-011-5276-1_27
    DOI: 10.1007/978-94-011-5276-1_27
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