Browse > Article
http://dx.doi.org/10.4134/JKMS.2004.41.5.795

SOME INEQUALITIES ON TOTALLY REAL SUBMANIFOLDS IN LOCALLY CONFORMAL KAEHLER SPACE FORMS  

Alfonso, Carriazo (Department of Geometry and Topology Faculty of Mathematics)
Kim, Young-Ho (Fepartment of Mathematics College of Natural Sciences Kyungpook National University)
Yoon, Dae-Won (Department of Mathematics Education and RINS Gyeongsang National University)
Publication Information
Journal of the Korean Mathematical Society / v.41, no.5, 2004 , pp. 795-808 More about this Journal
Abstract
In this article, we establish sharp relations between the sectional curvature and the shape operator and also between the k-Ricci curvature and the shape operator for a totally real submanifold in a locally conformal Kaehler space form of constant holomorphic sectional curvature with arbitrary codimension. mean curvature, sectional curvature, shape operator, k-Ricci curvature, locally conformal Kaehler space form, totally real submanifold.
Keywords
mean curvature; sectional curvature; shape operator; k-Ricci curvature; locally conformal Kaeher space form; totally real submanifold;
Citations & Related Records
Times Cited By KSCI : 1  (Citation Analysis)
Times Cited By Web Of Science : 0  (Related Records In Web of Science)
Times Cited By SCOPUS : 2
연도 인용수 순위
1 B.-Y. Chen, Mean curvature and shape operator of isometric immersions in realspace-forms, Glasg. Math. J. 38 (1996), 87-97   DOI
2 B.-Y. Chen, Relations between Ricci curvature and shape operator for submanifolds with arbitrary codimensions, Glasg. Math. J. 41 (1999), 33-41   DOI
3 T. Kashiwada, Some properties of locally conformal Kähler manifolds, Hokkaido Math. J. 8 (1979), 191-198.   DOI
4 Y. H. Kim, C. W. Lee and D. W. Yoon, Shape operator of slant submanifolds in Sasakian spaces, Bull. Korean Math. Soc. 40 (2003), 63-76   과학기술학회마을   DOI   ScienceOn
5 K. Matsumoto and I. Mihai, An obstruction to the existence of minimal totally real immersions in a locally conformal Kähler space form, Bull. Yamagata Univ. Natur. Sci. 14 (1997), no. 2, 83-87
6 K. Matsumoto, I. Mihai and A. Oiaga, Shape operator $A_H$ for slant submanifolds in complex space forms, Bull. Yamagata Univ. Natur. Sci. 14 (2000), no. 4, 169-177
7 I. Vaisman, On locally conformal Kähler manifolds, Israel J. Math. 24 (1976), 338–351   DOI
8 K. Yano and M. Kon, Structures on manifolds, World Scientific, 1984