Hostname: page-component-7479d7b7d-jwnkl Total loading time: 0 Render date: 2024-07-09T05:13:30.584Z Has data issue: false hasContentIssue false
  • English
  • Français

A class of C-totally real submanifolds of Sasakian space forms

Part of: Global differential geometry

Published online by Cambridge University Press:  09 April 2009

Filip Defever ,
Ion Mihai  and
Leopold Verstraelen
Filip Defever
Affiliation:
Zuivere en Toegepaste Differentiaalmeetkunde, Department Wiskunde, K. U. Leuven, Celestijnenlaan 200 B, B-3001 Leuven, Belgium e-mail: filip.defever@wis.kuleuven.ac.be
Ion Mihai
Affiliation:
Faculty of Mathematics, University of Bucharest, Str. Academiei 14, 70109 Bucharest, Romania e-mail: imihai@math.math.unibuc.ro
Leopold Verstraelen
Affiliation:
Departement Wiskunde, K. U. Leuven, Celestijnenlaan 200 B, B - 3001 Leuven, Belgium, and Group of Exact Sciences, K.U. Brussel, Vrijheidslaan, 17 B - 1081 BrusselBelgium e-mail: leopold.verstraelen@wis.kuleuven.ac.be
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

Recently, Chen defined an invariant δM of a Riemannian manifold M. Sharp inequalities for this Riemannian invariant were obtained for submanifolds in real, complex and Sasakian space forms, in terms of their mean curvature. In the present paper, we investigate certain C-totally real submanifolds of a Sasakian space form M2m+1(C)satisfying Chen's equality.

MSC classification

Secondary: 53C15: General geometric structures on manifolds (almost complex, almost product structures, etc.) 53C40: Global submanifolds 53C25: Special Riemannian manifolds (Einstein, Sasakian, etc.)
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 65 , Issue 1 , August 1998 , pp. 120 - 128
Copyright
Copyright © Australian Mathematical Society 1998

References

[1]Blair, D. E., Contact manifolds in Riemannian geometry, Lecture Notes in Math. 509 (Springer, Berlin, 1976).CrossRefGoogle Scholar
[2]Chen, B.-Y., ‘Some pinching and classification theorems for minimal submanifolds’, Arch. Math. (Basel) 60(1993), 568–578.CrossRefGoogle Scholar
[3]Chen, B.-Y., ‘A Riemannian invariant for submanfolds in space forms and its applications (World Scientific, Singapore, 1994) pp. 58–81.Google Scholar
[4]Chen, B.-Y., Dillen, F., Verstraelen, L. and Vrancken, L., ‘Totally real submanifolds of CPn satisfying a basic equality’, Arch. Math. (Basel) 63 (1994), 553–564.CrossRefGoogle Scholar
[5]Chen, B.-Y., Dillen, F., Verstraelen, L. and Vrancken, L., ‘Characterizing a class of totally real submanifolds of S 6(1) by their sectional curvatures’, Tôhoku Math. J. 47 (1995), 185–198.CrossRefGoogle Scholar
[6]Chen, B.-Y., Dillen, F., Verstraelen, L. and Vrancken, L., ‘An exotic totally real minimal immersion of S 3 in CP 3 and its characterization’, Proc. Roy. Soc. Edinburgh Sect. A 126 (1996), 153–165.CrossRefGoogle Scholar
[7]Defever, F., Mihai, I. and Verstraelen, L., ‘B.-Y. Chen's inequality for C-totally real submanifolds of Sasakian space forms’, Boll. Un. Mat. Ital. B 11 (1997), 365–374.Google Scholar
[8]Hiepko, S., ‘Eine innere Kennzeichung der verzerrten Produkte’, Math. Ann. 241 (1979), 209–215.CrossRefGoogle Scholar
[9]Yano, K. and Kon, M., Anti-invariant submanifolds, Lecture Notes in Pure and AppI. Math. (Marcel Dekker, New York, 1976).Google Scholar
[10]Yano, K. and Kon, M., Structures on manifolds, Ser. Pure Math. 3 (World Scientific, Singapore, 1984).Google Scholar