DOI QR코드

DOI QR Code

CONTACT CR-WARPED PRODUCT SUBMANIFOLDS IN KENMOTSU SPACE FORMS

  • ARSLAN, KADRI ;
  • EZENTAS, RIDVAN ;
  • MIHAl, ION ;
  • MURATHAN, CENGIZHAN
  • Published : 2005.09.01

Abstract

Recently, Chen studied warped products which are CR-submanifolds in Kaehler manifolds and established general sharp inequalities for CR-warped products in Kaehler manifolds. In the present paper, we obtain sharp estimates for the squared norm of the second fundamental form (an extrinsic invariant) in terms of the warping function for contact CR-warped products isometrically immersed in Kenmotsu space forms. The equality case is considered. Some applications are derived.

Keywords

contact CR-submanifold ;warped product;Kenmotsu manifold;Kenmotsu space form

References

  1. K. Arslan, R. Ezentas, I. Mihai, C. Murathan and C. Ozgur, Ricci curvature of submanifolds in Kenmotsu space forms, Int. J. Math. Math. Sci. 29 (2002), 719-726 https://doi.org/10.1155/S0161171202012863
  2. D. E. Blair, Contact Manifolds in Riemannian Geometry, Lecture Notes in Math. 509, Springer, Berlin, 1976
  3. D. E. Blair and B. Y. Chen, On CR-submanifolds of Hermitian manifolds, Israel J. Math. 34 (1979), 353-363 https://doi.org/10.1007/BF02760614
  4. B. Y. Chen, CR-submanifolds of a Kaehler manifold, J. Differential Geom. 16 (1981), 305-323 https://doi.org/10.4310/jdg/1214436106
  5. B. Y. Chen, Geometry of warped products as Riemannian submanifolds and related problems, Soochow J. Math. 28 (2002), 125-156
  6. B. Y. Chen, Geometry of warped product CR-submanifolds in Kaehler manifolds, Monatsh. Math. 133 (2001), 177-195 https://doi.org/10.1007/s006050170019
  7. B. Y. Chen, On isometric minimal immersions from warped products into real space forms, Proc. Edinb. Math. Soc. (2) 45 (2002), 579-587
  8. B. Y. Chen, Some pinching and classification theorems for minimal submanifolds, Arch. Math. 60 (1993), 568-578 https://doi.org/10.1007/BF01236084
  9. B. Y. Chen and K. Ogiue, On totally real submanifolds, Trans. Amer. Math.Soc. 193 (1974), 257-266
  10. I. Hasegawa and I. Mihai, Contact CR-warped product submanifolds in Sasakian manifolds, Geom. Dedicata 102 (2003), 143-150 https://doi.org/10.1023/B:GEOM.0000006582.29685.22
  11. K. Kenmotsu, A class of almost contact Riemannian manifolds, Tohoku Math. J. 24 (1972), 93-103 https://doi.org/10.2748/tmj/1178241594
  12. A. Mihai, Warped product submanifolds in complex space forms, Acta Sci. Math. (Szeged) 70 (2004), 419-427
  13. K. Yano and M. Kon, Structures on Manifolds, World Scientific, Singapore, 1984
  14. B. Y. Chen, CR-warped products in complex projective spaces with compact holomorphic factor, Monatsh. Math. 141 (2004), 177-186 https://doi.org/10.1007/s00605-002-0009-y
  15. S. Nolker, Isometric immersions of warped products, Differential Geom. Appl. 6 (1996), 1-30 https://doi.org/10.1016/0926-2245(96)00004-6
  16. S. Tanno, The automorphisms groups of almost contact metric manifolds, Tohoku Math. J. 21 (1969), 21-38 https://doi.org/10.2748/tmj/1178243031

Cited by

  1. Geometry of warped product semi-slant submanifolds of Kenmotsu manifolds 2017, https://doi.org/10.1007/s13373-017-0106-9
  2. Another class of warped product submanifolds of Kenmotsu manifolds 2017, https://doi.org/10.1007/s13398-017-0415-6
  3. Geometry of warped product immersions of Kenmotsu space forms and its applications to slant immersions vol.114, 2017, https://doi.org/10.1016/j.geomphys.2016.12.001
  4. Contact CR-warped product submanifolds in cosymplectic space forms vol.62, pp.1, 2011, https://doi.org/10.1007/s13348-010-0002-z
  5. Contact CR-Warped product Submanifolds in Cosymplectic Manifolds vol.56, pp.3, 2016, https://doi.org/10.5666/KMJ.2016.56.3.965
  6. CR-warped product submanifolds of a generalized complex space form vol.4, pp.1, 2017, https://doi.org/10.1080/23311835.2017.1306153
  7. A note on doubly warped product contact C R-submanifolds in trans-Sasakian manifolds vol.116, pp.1-2, 2007, https://doi.org/10.1007/s10474-007-6013-x
  8. A note on warped product submanifolds of Kenmotsu manifolds vol.61, pp.1, 2011, https://doi.org/10.2478/s12175-010-0061-3
  9. B.-Y. Chen’s Inequality for Bi-warped Products and Its Applications in Kenmotsu manifolds vol.15, pp.5, 2018, https://doi.org/10.1007/s00009-018-1238-1
  10. Geometry of warped product pseudo-slant submanifolds of Kenmotsu manifolds pp.1727-933X, 2018, https://doi.org/10.2989/16073606.2018.1452800
  11. Warped product semi-slant submanifolds of a locally product Riemannian manifold vol.46, pp.2, 2009, https://doi.org/10.1556/SScMath.46.2009.2.1086
  12. Semi-invariant warped product submanifolds of almost contact manifolds vol.2012, pp.1, 2012, https://doi.org/10.1186/1029-242X-2012-127
  13. On Casorati Curvatures of Submanifolds in Pointwise Kenmotsu Space Forms vol.22, pp.1, 2019, https://doi.org/10.1007/s11040-018-9297-x
  14. Classification of Warped Product Submanifolds in Kenmotsu Space Forms Admitting Gradient Ricci Solitons vol.7, pp.2, 2019, https://doi.org/10.3390/math7020112