DIRECTED RIEMANNIAN MANIFOLDS OF POINTWISE CONSTANT RELATIVE SECTIONAL CURVATURE

作者：Ganchev Georgi^*; Mihova Vesselka

来源：Comptes Rendus de l Academie Bulgare des Sciences, 2013, 66(11): 1505-1514.

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

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%26apos;s type.

• 出版日期2013