Proceedings of the International Geometry Center

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Warped product semi-slant submanifolds in locally conformal Kaehler manifolds

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Koji Matsumoto

Abstract

In 1994, in [13], N. Papaghiuc introduced the notion of semi-slant submanifold in a Hermitian manifold which is a generalization of CR- and slant-submanifolds. In particular, he considered this submanifold in Kaehlerian manifolds, [13]. Then, in 2007, V. A. Khan and M. A. Khan considered this submanifold in a nearly Kaehler manifold and obtained interesting results, [11]. Recently, we considered semi-slant submanifolds in a locally conformal Kaehler manifold and gave a necessary and sufficient conditions for two distributions (holomorphic and slant) to be integrable. Moreover, we considered these submanifolds in a locally conformal Kaehler space form, [4]. In this paper, we define 2-kind warped product semi-slant submanifolds in a locally conformal Kaehler manifold and consider some properties of these submanifolds.

Keywords:
Locally conformal Kaehler manifold, slant distribution, semi-slant submanifold, warped product semi-slant submanifold

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How to Cite
Matsumoto, K. (2017). Warped product semi-slant submanifolds in locally conformal Kaehler manifolds. Proceedings of the International Geometry Center, 10(2). https://doi.org/10.15673/tmgc.v10i2.650
Section
Papers
Author Biography

Koji Matsumoto, Emeritus at Yamagata University, Member of "Tensor Society", Cooperator of the Journal "Tensor Japan ", (Japan Yamagata)

Ph. D. in phys. and math.  sciences, professor

References

1. Aurel Bejancu. CR submanifolds of a Kaehler manifold. I. Proc. Amer. Math. Soc., 69(1):135–142, 1978.

2. Aurel Bejancu. CR submanifolds of a Kaehler manifold. II. Trans. Amer. Math. Soc., 250:333–345, 1979.

3. Aurel Bejancu. Geometry of CR-submanifolds, volume 23 of Mathematics and its Applications(East European Series). D. Reidel Publishing Co., Dordrecht, 1986.

4. Vittoria Bonanzinga, Koji Matsumoto. Semi-slant submanifolds in locally conformal Kaehler manifolds. to appear.

5. Vittoria Bonanzinga, Koji Matsumoto. Warped product CR-submanifolds in locally conformal Kaehler manifolds. Period. Math. Hungar., 48(1-2):207–221, 2004.

6. Bang-Yen Chen. Geometry of submanifolds. Marcel Dekker, Inc., New York, 1973. Pure and Applied Mathematics, No. 22.

7. Bang-Yen Chen. CR-submanifolds of a Kaehler manifold. I. J. Differential Geom., 16(2):305–322, 1981.

8. Bang-Yen Chen. CR-submanifolds of a Kaehler manifold. II. J. Differential Geom., 16(3):493–509 (1982), 1981.

9. Bang-Yen Chen. Geometry of slant submanifolds. Katholieke Universiteit Leuven, Louvain, 1990.

10. Toyoko Kashiwada. Some properties of locally conformal Kähler manifolds. HokkaidoMath. J., 8(2):191–198, 1979.

11. Viqar Azam Khan, Meraj Ali Khan. Semi-slant submanifolds of a nearly Kaehler manifold. Turkish J. Math., 31(4):341–353, 2007.

12. Barrett O’Neill. Semi-Riemannian geometry, volume 103 of Pure and Applied Mathematics. Academic Press, Inc. [Harcourt Brace Jovanovich, Publishers], New York, 1983. With applications to relativity.

13. Neculai Papaghiuc. Semi-slant submanifolds of a Kaehlerian manifold. An. Ştiinţ. Univ. Al. I. Cuza Iaşi Secţ. I a Mat., 40(1):55–61, 1994.

14. Izu Vaisman. On locally conformal almost Kähler manifolds. Israel Journal of Mathematics, 24(3-4):338–351, Dec 1976.