Surveys in Mathematics and its Applications

ISSN 1842-6298 (electronic), 1843-7265 (print)
 Volume 5 (2010), 201 -- 213

SEMI-INVARIANT SUBMANIFOLDS OF (g,F)-MANIFOLDS

Novac-Claudiu Chiriac

Abstract. We introduce (g,F)-manifolds and initiate a study of their semi-invariant submanifolds. These submanifolds are generalizations of CR-submanifolds of Kaehler manifolds. We obtain necessary and sufficient conditions for the integrability of distributions on a semi-invariant submanifold and study the geometry of foliations defined by these distributions. In particular, for a large class of (g,F)-manifolds we prove the existence of a natural foliation on their semi-invariant submanifolds.

2010 Mathematics Subject Classification: 53C40, 53C15.
Keywords: semi-invariant submanifold; (g,F)-manifold; Distribution; Foliation.

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References

  1. C.L. Bejan, CR-Submanifolds of hyperbolic almost Hermitian manifolds, Demonstratio Mathematica, 23 (1990), 335-343. MR1101496 (92b:53036). Zbl 0754.53023.

  2. A. Bejancu, CR-Submanifolds of a Kaehler manifold I, Proc. Amer. Math. Soc., 69 (1978), 134-142. MR0467630 (57 #7486). Zbl 0368.53040.

  3. A. Bejancu, Geometry of CR-Submanifolds, D. Reidel Publish. Comp., Dordrecht, 1986. MR0861408 (87k:53126). Zbl 0605.53001.

  4. A. Bejancu and N. Papaghiuc, Semi-invariant submanifolds of a Sasakian manifold, An. St. Univ. \textquotedblright Al. I. Cuza\textquotedblright Iaşi, 27 (1981), 163-170. MR0618723(82i:53037).

  5. D.E. Blair, Riemannian Geometry of Contact and Symplectic Manifolds, Birkhäuser, Boston, 2002. MR1874240 (2002m:53120). Zbl 1011.53001.

  6. D.E. Blair and B.Y. Chen, On CR-submanifolds of Hermitian manifolds, Israel J. Math., 34 (1979), 353-363. MR0570892(81f:53049). Zbl 0453.53018.

  7. B.Y. Chen, Geometry of Submanifolds and Its Applications, Science Univ. Tokyo, 1981. MR0627323 (82m:53051). Zbl 0474.53050.

  8. S. Ianuş and I. Mihai, Semi-invariant submanifolds of an almost paracontact manifolds, Tensor N.S., 39 (1982), 195-200. MR0836935 (87c:53102). Zbl 0514.53015.

  9. B. O'Neill, Semi-Riemannian Geometry with Applications to Relativity, Academic Press, New York, 1983. MR0719023(85f:53002). Zbl 0531.53051.

  10. I. Sato, On a structure similar to the almost contact structure, Tensor, 30 (1976), 219-224. MR0442845(56 #1221). Zbl 0344.53025

  11. K. Yano and M. Kon, CR-Submanifolds of Kaehlerian and Sasakian Manifolds, Birkhäuser, Boston, 1983. MR0688816(84k:53051). Zbl 0496.53037.

  12. K. Yano and M. Kon, Structures on Manifolds, World Scientific, Singapore, 1984. MR0794310(86g:53001). Zbl 0557.53001.



\noindent Novac-Claudiu Chiriac
University Constantin Brâncuşi of Târgu-Jiu
Str. Geneva, Nr. 3, 210136 Târgu-Jiu, Romania.
e-mail: novac@utgjiu.ro
http://www.utgjiu.ro/math/nchiriac/

http://www.utgjiu.ro/math/sma