On the role of partial Ricci curvature in the geometry of submanifolds and foliations

• Autorzy: Vladimir Rovenskiĭ
• Języki publikacji: EN

Abstrakty

EN

Submanifolds and foliations with restrictions on q-Ricci curvature are studied. In §1 we estimate the distance between two compact submanifolds in a space of positive q-Ricci curvature, and give applications to special classes of submanifolds and foliations: k-saddle, totally geodesic, with nonpositive extrinsic q-Ricci curvature. In §2 we generalize a lemma by T. Otsuki on asymptotic vectors of a bilinear form and then estimate from below the radius of an immersed submanifold in a simply connected Riemannian space with nonpositive curvature; moreover, we prove a theorem on nonembedding into a circular cylinder when the ambient space is Euclidean. Corollaries are nonembedding theorems of Riemannian manifolds with nonpositive q-Ricci curvature into a Euclidean space. In §3 a lower estimate of the index of relative nullity of a submanifold with nonpositive extrinsic q-Ricci curvature is proven. Corollaries are extremal theorems for a compact submanifold with the nullity foliation in a Riemannian space of positive curvature. On the way, some results by T. Frankel, K. Kenmotsu and C. Xia, J. Morvan, A. Borisenko, S. Tanno, B. O'Neill, J. Moore, T. Ishihara, H. Jacobowitz, L. Florit, M. Dajczer and L. Rodríguez are generalized.

Słowa kluczowe

EN

Riemannian manifold; submanifold; foliation; ruled submanifold; q-Ricci curvature; distance; radius of submanifold; index of relative nullity

Kategorie tematyczne

• 53C12: Foliations (differential geometric aspects)
• 53C40: Global submanifolds

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Annales Polonici Mathematici
• Rocznik: 1998
• Tom: 68
• Numer: 1
• Strony: 61-82

Daty

wydano

1998

otrzymano

1996-11-28

Twórcy

autor

Vladimir Rovenskiĭ

• Geometry Chair, State Pedagogical University, Lebedeva St., 89 Krasnoyarsk 660049, Russia

Bibliografia

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