DIRECTED RIEMANNIAN MANIFOLDS OF POINTWISE CONSTANT RELATIVE SECTIONAL CURVATURE

被引：0

作者：

Ganchev, Georgi ^{[1
]}

Mihova, Vesselka ^{[2
]}

机构：

[1] Bulgarian Acad Sci, Inst Math & Informat, BU-1113 Sofia, Bulgaria

[2] St Kl Ohridski Univ Sofia, Fac Math & Informat, Sofia 1164, Bulgaria

来源：

COMPTES RENDUS DE L ACADEMIE BULGARE DES SCIENCES | 2013年 / 66卷 / 11期

关键词：

Riemannian manifolds with scalar distribution; sectional; 1-form; directed Riemannian manifolds; pointwise constant relative sectional curvature;

D O I：

暂无

中图分类号：

O [数理科学和化学]; P [天文学、地球科学]; Q [生物科学]; N [自然科学总论];

学科分类号：

07 ; 0710 ; 09 ;

摘要：

We study a class of Riemannian manifolds with respect to the covariant derivative of their curvature tensors. We introduce geometrically the class of directed Riemannian manifolds of pointwise constant relative sectional curvature and give a tensor characterization for such manifolds. We prove that all rotational hypersurfaces are directed and find the rotational hypersurfaces of pointwise constant relative sectional curvature. For the class of directed Riemannian manifolds of pointwise constant relative sectional curvature having a totally umbilical scalar distribution we prove a structural theorem and a theorem of Schur's type.

引用

页码：1505 / 1514

页数：10

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