Some results on the geometry of warped product CR-submanifolds in quasi-Sasakian manifold
- Shamsur Rahman shamsur@rediffmail.com
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DOI:
https://doi.org/10.4067/S0719-06462022000100105Abstract
The present paper deals with a study of warped product submanifolds of quasi-Sasakian manifolds and warped product CR-submanifolds of quasi-Sasakian manifolds. We have shown that the warped product of the type \( M = D_{\perp}{\times}{_{y}}{D}_{T}\) does not exist, where \( D_{\perp}\) and \( D_{T}\) are invariant and anti-invariant submanifolds of a quasi-Sasakian manifold \(\bar{M}\), respectively. Moreover we have obtained characterization results for CR-submanifolds to be locally CR-warped products.
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K. Arslan, R. Ezentas, I. Mihai and C. Murathan, “Contact CR-warped product submanifolds in Kenmotsu space forms”, J. Korean Math. Soc., vol. 42, no. 5, pp. 1101–1110, 2005.
A. Bejancu, “CR-submanifold of a Kaehler manifold. I”, Proc. Amer. Math. Soc., vol. 69, no. 1, 135–142, 1978.
A. Bejancu and N. Papaghiuc, “Semi-invariant submanifolds of a Sasakian manifold.”, An. ÅžtiinÅ£. Univ. “Al. I. Cuza” IaÅŸi SecÅ£. I a Mat. (N.S.), vol. 27, no. 1, pp. 163–170, 1981.
T.-Q. Binh and A. De, “On contact CR-warped product submanifolds of a quasi-Sasakian manifold”, Publ. Math. Debrecen, vol. 84, no. 1-2, pp. 123–137, 2014.
R. L. Bishop and B. O‘Neill, “Manifolds of negative curvature”, Trans. Amer. Math. Soc., vol. 145, pp. 1–49, 1969.
D. E. Blair, Contact manifolds in Riemannian geometry, Lecture Notes in Math., vol. 509, Berlin-New York: Springer-Verlag, 1976.
C. Calin, “Contributions to geometry of CR-submanifold”, PhD Thesis, University of IaÅŸi, IaÅŸi, Romania, 1998.
B.-Y. Chen, “Geometry of warped product CR-submanifolds in Kaehler manifolds”, Monatsh. Math., vol. 133, no. 3, pp. 177–195, 2001.
I. Hasegawa and I. Mihai, “Contact CR-warped product submanifolds in Sasakian manifolds”, Geom. Dedicata, vol. 102, pp. 143–150, 2003.
S. Hiepko, “Eine innere Kennzeichnung der verzerrten Produkte”, Math. Ann., vol. 241, no. 3, pp. 209–215, 1979.
M.-I. Munteanu, “A note on doubly warped product contact CR-submanifolds in trans-Sasakian manifolds”, Acta Math. Hungar., vol. 116, no. 1-2, pp. 121–126, 2007.
K. Yano, “On structure defined by a tensor field f of type (1, 1) satisfying f^3 + f = 0”, Tensor (N.S.), vol. 14, pp. 99–109, 1963.
K. Yano and M. Kon, Structures on manifolds, Series in Pure Mathematics, vol. 3, Singapore: World Scientific Publishing Co., 1984.