In this paper,kinematic formulae in a real space form are investigated.A kinematic formula for homogeneous polynomial of degree 4 on the second fundamental forms in a real space form is obtained.The formula obtained i...In this paper,kinematic formulae in a real space form are investigated.A kinematic formula for homogeneous polynomial of degree 4 on the second fundamental forms in a real space form is obtained.The formula obtained is a concrete form of the result of Howard and the analogue of the known formula of Chen and Zhou.展开更多
The purpose of this paper is to define a ruled real hypersurface of a complex space form M_n(c),c≠0,and to give characterizations of this hypersurface by the infinitesimal affine transformation of the structure vecto...The purpose of this paper is to define a ruled real hypersurface of a complex space form M_n(c),c≠0,and to give characterizations of this hypersurface by the infinitesimal affine transformation of the structure vector field induced on the hypersurface.展开更多
In this paper, the vertical and horizontal distributions of an invariant sub-manifold of a Riemannian product manifold are discussed. An invariant real space form in a Riemannian product manifold is researched. Finall...In this paper, the vertical and horizontal distributions of an invariant sub-manifold of a Riemannian product manifold are discussed. An invariant real space form in a Riemannian product manifold is researched. Finally, necessary and sufficient conditions are given on an invariant submanifold of a Riemannian product manifold to be a locally symmetric and real space form.展开更多
基金Supported in part by National Natural Science Foundation of China(Grant Nos.11126324,11271302,11161007,11326073)
文摘In this paper,kinematic formulae in a real space form are investigated.A kinematic formula for homogeneous polynomial of degree 4 on the second fundamental forms in a real space form is obtained.The formula obtained is a concrete form of the result of Howard and the analogue of the known formula of Chen and Zhou.
基金Supported by Grant for the Institute of Mathematicsthe University of Tsukuba and TGRC-KOSEF(1993)
文摘The purpose of this paper is to define a ruled real hypersurface of a complex space form M_n(c),c≠0,and to give characterizations of this hypersurface by the infinitesimal affine transformation of the structure vector field induced on the hypersurface.
基金Supported by the National Natural Science Foundation of China(11071005)Foundation for Excellent Young Talents of Higher Education(2011SQRL021ZD)+1 种基金the Natural Science Foundation of Anhui Educational Committee(KJ2010A125)the Natural Science Foundation of Anhui Educational Committee(KJ2012b197)
文摘In this paper, the vertical and horizontal distributions of an invariant sub-manifold of a Riemannian product manifold are discussed. An invariant real space form in a Riemannian product manifold is researched. Finally, necessary and sufficient conditions are given on an invariant submanifold of a Riemannian product manifold to be a locally symmetric and real space form.
