Journal of the Korean Mathematical Society (대한수학회지)

Korean Mathematical Society (대한수학회)
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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)
  • Published : 2004.09.01
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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

References

  1. B.-Y. Chen, Mean curvature and shape operator of isometric immersions in realspace-forms, Glasg. Math. J. 38 (1996), 87-97 https://doi.org/10.1017/S001708950003130X
  2. B.-Y. Chen, Relations between Ricci curvature and shape operator for submanifolds with arbitrary codimensions, Glasg. Math. J. 41 (1999), 33-41 https://doi.org/10.1017/S0017089599970271
  3. T. Kashiwada, Some properties of locally conformal Kähler manifolds, Hokkaido Math. J. 8 (1979), 191-198. https://doi.org/10.14492/hokmj/1381758270
  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 https://doi.org/10.4134/BKMS.2003.40.1.063
  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 https://doi.org/10.1007/BF02834764
  8. K. Yano and M. Kon, Structures on manifolds, World Scientific, 1984

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  1. On Chen invariants and inequalities in quaternionic geometry vol.2013, pp.1, 2013, https://doi.org/10.1186/1029-242X-2013-66