The Pure and Applied Mathematics (한국수학교육학회지시리즈B:순수및응용수학)

Korean Society of Mathematical Education (한국수학교육학회)
권호 표지

REAL HALF LIGHTLIKE SUBMANIFOLDS WITH TOTALLY UMBILICAL PROPERTIES

  • Jin, Dae-Ho (DEPARTMENT OF MATHEMATICS, DONGGUK UNIVERSITY)
  • Published : 2010.02.28
Download PDF
⟨ Previous Next ⟩

Abstract

In this paper, we prove two characterization theorems for real half lightlike submanifold (M,g,S(TM)) of an indefinite Kaehler manifold $\bar{M}$ or an indefinite complex space form $\bar{M}$(c) subject to the conditions : (a) M is totally umbilical in $\bar{M}$, or (b) its screen distribution S(TM) is totally umbilical in M.

Keywords

References

  1. Duggal, K.L. & Bejancu, A.: Lightlike submanifolds of codimension 2. Math. J. Toyama Univ. 15 (1992), 59-82.
  2. Duggal, K.L. & Bejancu, A.: Lightlike Submanifolds of Semi-Riemannian Manifolds and Applications. Kluwer Acad. Publishers, Dordrecht, 1996.
  3. Duggal, K.L. & Jin, D.H.: Half-lightlike submanifolds of codimension 2. Math. J. Toyama Univ. 22 (1999), 121-161.
  4. Jin, D.H.: Lightlike hypersurfaces with totally umbilical screen distributions. to appear in J. Chungcheong Math. Soc.
  5. Jin, D.H.: Half lightlike submanifolds with totally umbilical screen distributions. to appear in J. Korea Soc. Math. Educ. Ser. B: Pure Appl. Math.
  6. Jin, D.H.: Lightlike real hypersurfaces with totally umbilical screen distributions, to appear in Commun. Korean Math. Soc.
  7. Jin, D.H.: Geometry of screen conformal real half lightlike submanifolds. to appear in Bull. Korean Math. Soc.
  8. Kupeli, D.N.: Singular Semi-Riemannian Geometry. Mathematics and Its Applications, Kluwer Acad. Publishers, Dordrecht, 1996.
  9. O'Neill, B.: Semi-Riemannian Geometry with Applications to Relativity. Academic Press, 1983.