Hostname: page-component-6d856f89d9-xkcpr Total loading time: 0 Render date: 2024-07-16T08:42:45.554Z Has data issue: false hasContentIssue false
  • English
  • Français

Submanifolds satisfying some curvature conditions imposed on the Weyl tensor

Published online by Cambridge University Press:  17 April 2009

Cihan Özgür
Cihan Özgür
Affiliation:
Department of Mathematics, Balikesir University, 10100, Balikesir, Turkey, e-mail: cozgur@balikesir.edu.tr
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.

In this paper we define Weyl semiparallel ( · h = 0) and Weyl 2-semiparallel ( · h = 0) submanifolds. We consider n-dimensional normally flat submanifolds satisfying these curvature conditions in (n + d)-dimensional Euclidean space n+d. We also consider normally flat submanifolds in (n + d)-dimensional Euclidean space n+d satisfying the condition  · h = LQ (g, h) and  · h = LQ(g, h).

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 67 , Issue 1 , February 2003 , pp. 95 - 101
Copyright
Copyright © Australian Mathematical Society 2003

References

REFERENCES

[1]Arslan, K., Lumiste, Ü., Murathan, C. and Özgür, C., ‘2-semiparallel surfaces in space forms. I. Two particular cases’, Proc. Estonian Acad. Sci. Phys. Math. 49 (2000), 139–148.CrossRefGoogle Scholar
[2]Chen, B.Y., Geometry of submanifolds (Marcel Dekker, New York, 1973).Google Scholar
[3]Chen, B.Y. and Yano, K., ‘Sous-variétés localement conformes à un espace euclidien’, C. R. Acad. Sci. Paris Ser. A-B 275 (1972), Paris.Google Scholar
[4]Deprez, J., ‘Semi-parallel surfaces in the Euclidean space’, J. Geom. 25 (1985), 192–200.CrossRefGoogle Scholar
[5]Deprez, J., ‘Semi-parallel hypersurfaces’, Rend. Sem. Mat. Univ. Politec. Torino 44 (1986), 303–316.Google Scholar
[6]Deszcz, R., ‘On pseudosymmetric spaces’, Bull. Soc. Math. Belg. A 44 (1992), 1–34.Google Scholar
[7]Lumiste, Ü., ‘2-semiparallel surfaces in space forms II. The general case’, Proc. Estonian Acad. Sci. Phys. Math. 49 (2000), 203–214.CrossRefGoogle Scholar
[8]Verstraelen, L. and Zafindrafata, G., ‘Some comments on conformally flat submanifolds’, in Geometry and Topology of Submanifolds 3 (World Sci., River Edge, NJ, 1991), PP. 312–314.Google Scholar