Slant and pseudo-slant submanifolds in -manifolds

Mehmet Atçeken; Shyamal Kumar Hui

Czechoslovak Mathematical Journal (2013)

  • Volume: 63, Issue: 1, page 177-190
  • ISSN: 0011-4642

Abstract

top
We show new results on when a pseudo-slant submanifold is a LCS-manifold. Necessary and sufficient conditions for a submanifold to be pseudo-slant are given. We obtain necessary and sufficient conditions for the integrability of distributions which are involved in the definition of the pseudo-slant submanifold. We characterize the pseudo-slant product and give necessary and sufficient conditions for a pseudo-slant submanifold to be the pseudo-slant product. Also we give an example of a slant submanifold in an LCS-manifold to illustrate the subject.

How to cite

top

Atçeken, Mehmet, and Kumar Hui, Shyamal. "Slant and pseudo-slant submanifolds in ${\rm LCS}$-manifolds." Czechoslovak Mathematical Journal 63.1 (2013): 177-190. <http://eudml.org/doc/252505>.

@article{Atçeken2013,
abstract = {We show new results on when a pseudo-slant submanifold is a LCS-manifold. Necessary and sufficient conditions for a submanifold to be pseudo-slant are given. We obtain necessary and sufficient conditions for the integrability of distributions which are involved in the definition of the pseudo-slant submanifold. We characterize the pseudo-slant product and give necessary and sufficient conditions for a pseudo-slant submanifold to be the pseudo-slant product. Also we give an example of a slant submanifold in an LCS-manifold to illustrate the subject.},
author = {Atçeken, Mehmet, Kumar Hui, Shyamal},
journal = {Czechoslovak Mathematical Journal},
keywords = {slant submanifold; pseudo-slant submanifold; $\{\rm LCS\}$-manifold; slant submanifold; pseudo-slant submanifold; -manifold},
language = {eng},
number = {1},
pages = {177-190},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Slant and pseudo-slant submanifolds in $\{\rm LCS\}$-manifolds},
url = {http://eudml.org/doc/252505},
volume = {63},
year = {2013},
}

TY - JOUR
AU - Atçeken, Mehmet
AU - Kumar Hui, Shyamal
TI - Slant and pseudo-slant submanifolds in ${\rm LCS}$-manifolds
JO - Czechoslovak Mathematical Journal
PY - 2013
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 63
IS - 1
SP - 177
EP - 190
AB - We show new results on when a pseudo-slant submanifold is a LCS-manifold. Necessary and sufficient conditions for a submanifold to be pseudo-slant are given. We obtain necessary and sufficient conditions for the integrability of distributions which are involved in the definition of the pseudo-slant submanifold. We characterize the pseudo-slant product and give necessary and sufficient conditions for a pseudo-slant submanifold to be the pseudo-slant product. Also we give an example of a slant submanifold in an LCS-manifold to illustrate the subject.
LA - eng
KW - slant submanifold; pseudo-slant submanifold; ${\rm LCS}$-manifold; slant submanifold; pseudo-slant submanifold; -manifold
UR - http://eudml.org/doc/252505
ER -

References

top
  1. Atçeken, M., 10.1016/S0252-9602(10)60039-2, Acta Math. Sci., Ser. B, Engl. Ed. 30 (2010), 215-224. (2010) MR2658956DOI10.1016/S0252-9602(10)60039-2
  2. Bishop, R. L., O'Neill, B., 10.1090/S0002-9947-1969-0251664-4, Trans. Am. Math. Soc. 145 (1969), 1-49. (1969) Zbl0191.52002MR0251664DOI10.1090/S0002-9947-1969-0251664-4
  3. Cabrerizo, J. L., Carriazo, A., Fernández, L. M., Fernández, M., 10.1023/A:1005241320631, Geom. Dedicata 78 (1999), 183-199. (1999) Zbl0944.53028MR1722833DOI10.1023/A:1005241320631
  4. Cabrerizo, J. L., Carriazo, A., Fernández, L. M., Fernández, M., Structure on a slant submanifold of a contact manifold, Indian J. Pure Appl. Math. 31 (2000), 857-864. (2000) Zbl0984.53034MR1779445
  5. Carriazo, A., Fernández, L. M., Hans-Uber, M. B., 10.1007/s10474-005-0195-x, Acta Math. Hung. 107 (2005), 267-285. (2005) Zbl1120.53027MR2150790DOI10.1007/s10474-005-0195-x
  6. Chen, B. Y., Geometry of Slant Submanifolds, Kath. Univ. Leuven, Dept. of Mathematics Leuven (1990). (1990) Zbl0716.53006MR1099374
  7. Khan, V. A., Khan, M. A., Pseudo-slant submanifolds of a Sasakian manifold, Indian J. Pure Appl. Math. 38 (2007), 31-42. (2007) Zbl1117.53043MR2333574
  8. Lotta, A., Slant submanifolds in contact geometry, Bull. Math. Soc. Sci. Math. Roum., Nouv. Sér. 39 (1996), 183-198. (1996) Zbl0885.53058
  9. Matsumoto, K., Mihai, I., On a certain transformation in a Lorentzian para-Sasakian manifold, Tensor, New Ser. 47 (1988), 189-197. (1988) Zbl0679.53034MR1004844
  10. Mihai, I., Chen, B. Y., 10.1007/s10474-008-8033-6, Acta Math. Hung. 122 (2009), 307-328. (2009) Zbl1199.53167MR2481783DOI10.1007/s10474-008-8033-6
  11. Papaghiuc, N., Semi-slant submanifolds of a Kaehlerian manifold, An. Ştiinţ. Univ. Al. I. Cuza Iaşi, Ser. Nouǎ, Mat. 40 (1994), 55-61. (1994) Zbl0847.53012MR1328947
  12. Shaikh, A. A., On Lorentzian almost paracontact manifolds with a structure of the concircular type, Kyungpook Math. J. 43 (2003), 305-314. (2003) Zbl1054.53056MR1983436
  13. Shaikh, A. A., Baishya, K. K., 10.3844/jmssp.2005.129.132, J. Math. Stat. 1 (2005), 129-132. (2005) Zbl1142.53326MR2197611DOI10.3844/jmssp.2005.129.132
  14. Shaikh, A. A., Kim, H. Y., Hui, S. K., 10.4134/JKMS.2011.48.4.669, J. Korean Math. Soc. 48 (2011), 669-689. (2011) Zbl1227.53030MR2840519DOI10.4134/JKMS.2011.48.4.669
  15. Yano, K., Concircular geometry. 1. Concircular transformations, Proc. Imp. Acad. Jap. 16 (1940), 195-200. (1940) Zbl0024.08102MR0003113

NotesEmbed ?

top

You must be logged in to post comments.