Acta mathematica scientia,Series B ›› 2004, Vol. 24 ›› Issue (4): 549-558.
• Articles • Previous Articles Next Articles
M. Atceken, S. Keles
Online:
Published:
Abstract:
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.
Key words: Riemannian product manifold, mixed geodesic submanifold, real space form and almost Riemannian product structure
CLC Number:
M. Atceken, S. Keles. ON THE INVARIANT SUBMANIFOLDS OF RIEMANNIAN PRODUCT MANIFOLD[J].Acta mathematica scientia,Series B, 2004, 24(4): 549-558.
Add to citation manager EndNote|Reference Manager|ProCite|BibTeX|RefWorks
URL: http://121.43.60.238/sxwlxbB/EN/
http://121.43.60.238/sxwlxbB/EN/Y2004/V24/I4/549
[1] Atceken M, Keles S. Two Theorems on Invariant Submanifolds of Riemannian Product Manifold. Indian J Pure and Appl Math, 2003, 34(7): 1035-1044 [2] Chen B Y. Total Mean Curvature and Submanifolds of Finite Type. World Scientific Publishing Co Pte Ltd, 1984 [3] Chen B Y. Geometry of Submanifolds. New York: Marcel Dekker Inc, 1973 [4] Matsumoto K. On Submanifolds of Locally Product Riemannian Manifolds. TRU Mathematics, 1982, 18(2): 145-157 [5] Rovenski V. Foliations on Riemannians Manifolds and Submanifolds. Boston: Birkhauser, 1997 [6] Xu Senlin, Ni Yilong. Submanifolds of Product Riemannian Manifolds. Acta Math Sci, 2000, 20B(2): 213-218
Cited