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On 3-dimensional contact slant submanifolds in Sasakian space forms

Published online by Cambridge University Press:  17 April 2009

Ion Mihai  and
Yoshihiko Tazawa
Ion Mihai
Affiliation:
Faculty of Mathematics, Str. Academiei 14, 70109 Bucharest, Romania, e-mail: imihai@math.math.unibuc.ro
Yoshihiko Tazawa
Affiliation:
School of Information Environment, Tokyo Denki University, Inzai, Chiba Prefecture 270-1382, Japan, e-mail: tazawa@cck.dendai.ac.jp
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Abstract

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Recently, B.-Y. Chen obtained an inequality for slant surfaces in complex space forms. Further, B.-Y. Chen and one of the present authors proved the non-minimality of proper slant surfaces in non-flat complex space forms. In the present paper, we investigate 3-dimensional proper contact slant submanifolds in Sasakian space forms. A sharp inequality is obtained between the scalar curvature (intrinsic invariant) and the main extrinsic invariant, namely the squared mean curvature.

It is also shown that a 3-dimensional contact slant submanifold M of a Sasakian space form (c), with c ≠ 1, cannot be minimal.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 68 , Issue 2 , October 2003 , pp. 275 - 283
Copyright
Copyright © Australian Mathematical Society 2003

References

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