On spherical submanifolds with nullity

Authors:
Marcos Dajczer and Detlef Gromoll

Journal:
Proc. Amer. Math. Soc. **93** (1985), 99-100

MSC:
Primary 53C42; Secondary 53C40

MathSciNet review:
766536

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Abstract: We derive a new condition for spherical submanifolds with positive relative nullity. As an application we obtain that the Ricci curvature is bounded from above by the curvature of the ambient space.

**[A]**Kinetsu Abe,*Some remarks on a class of submanifolds in space forms of nonnegative curvature*, Math. Ann.**247**(1980), no. 3, 275–278. MR**568992**, 10.1007/BF01348959**[F]**Dirk Ferus,*Isometric immersions of constant curvature manifolds*, Math. Ann.**217**(1975), no. 2, 155–156. MR**0407769****[M]**Reiko Miyaoka,*Complete hypersurfaces in the space form with three principal curvatures*, Math. Z.**179**(1982), no. 3, 345–354. MR**649037**, 10.1007/BF01215336**[O'N-S]**Barrett O’Neill and Edsel Stiel,*Isometric immersions of constant curvature manifolds*, Michigan Math. J.**10**(1963), 335–339. MR**0158329****[R]**Lucio L. Rodriguez,*Immersions of nonzero relative nullity in manifolds of constant positive curvature*, Arch. Math. (Basel)**32**(1979), no. 2, 181–184. MR**534930**, 10.1007/BF01238487

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DOI:
https://doi.org/10.1090/S0002-9939-1985-0766536-0

Article copyright:
© Copyright 1985
American Mathematical Society