Abstract.
Let \(\widetilde{M}^{2n+1}(c)\) be (2n + 1)-dimensional Sasakian space form of constant ϕ-sectional curvature (c) and M n be an n-dimensional C-totally real, minimal submanifold of \(\widetilde{M}^{2n+1}(c)\). We prove that if M n is pseudo-parallel and \(Ln-\frac{1}{4}(n(c + 3) + c - 1)\ge 0\), then M n is totally geodesic.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
AC Asperti GA Lobos F Mercuri (1999) ArticleTitlePseudo-paralel immersions in space forms Math Contemp 17 59–70 Occurrence Handle0976.53019 Occurrence Handle1787819
AC Asperti GA Lobos F Mercuri (2002) ArticleTitlePseudo-parallel immersions of a space form Adv Geom 2 57–71 Occurrence Handle1030.53058 Occurrence Handle10.1515/advg.2001.027 Occurrence Handle1880001
Blair DE (1976) Contact Manifolds in Riemannian Geometry. Lect Notes Math 509. Berlin Heibelberg New York: Springer
DE Blair K Ogiue (1975) ArticleTitlePositively curved integral submanifolds of a contact distribution Illinois J Math 19 628–631 Occurrence Handle0317.53049 Occurrence Handle383298
DE Blair K Ogiue (1975) ArticleTitleGeometry of integral submanifolds of a contact distribution Illinois J Math 19 269–276 Occurrence Handle0335.53043 Occurrence Handle377758
E Boeckx O Kowalski L Vanhecke (1996) Riemannian Manifolds of Conullity Two World Scientific Singapore Occurrence Handle0904.53006
BY Chen (1973) Geometry of Submanifolds Dekker New York Occurrence Handle0262.53036
J Deprez (1985) ArticleTitleSemi-parallel surfaces in euclidean space J Geom 25 192–200 Occurrence Handle0582.53042 Occurrence Handle10.1007/BF01220480 Occurrence Handle821680
J Deprez (1986) ArticleTitleSemi-parallel hypersurfaces Rend Sem Mat Univers Politecnico Torino 44 303–316 Occurrence Handle0616.53018 Occurrence Handle906021
A Derdzinski W Rotter (1977) ArticleTitleOn conformally symmetric manifolds with metrics of indices 0 and 1 Tensor NS 31 256–259
R Deszcz (1992) ArticleTitleOn pseudosymmetric spaces Bull Soc Belg Math Ser A 44 1–34 Occurrence Handle0808.53012 Occurrence Handle1315367
R Deszcz L Verstralen S Yaprak (1994) ArticleTitlePseudosymmetric hypersurfaces in 4-dimensional space of constant curvature Bull Ins Math Acad Sinica 22 167–179 Occurrence Handle0811.53014
F Dillen (1991) ArticleTitleSemi-parallel hypersurfaces of a real space form Israel J Math 75 193–202 Occurrence Handle0765.53012 Occurrence Handle1164590
F Dillen L Vrancken (1990) ArticleTitle C-Totally real submanifolds of Sasakian space forms J Math Pures Appl 69 85–93 Occurrence Handle0654.53062 Occurrence Handle1054125
D Ferus (1974) ArticleTitleImmersions with parallel second fundamental form Math Z 140 87–93 Occurrence Handle0279.53048 Occurrence Handle10.1007/BF01218650 Occurrence Handle370437
M Kon (1976) ArticleTitleRemarks on anti-invariant submanifolds of a Sasakian manifold Tensor 30 239–246 Occurrence Handle0344.53016 Occurrence Handle431004
O Kowalski (1996) ArticleTitleAn explicit classification of 3-dimensional Riemannian spaces satisfying R(X, Y)· R = 0 Czechoslovak Math J 46 427–474 Occurrence Handle0879.53014 Occurrence Handle1408298
Ü Lumiste (1990) ArticleTitleSemi-symmetric submanifolds as the second order envelope of symmetric submanifolds Proc Estonian Acad Sci Phys Math 39 1–8 Occurrence Handle0704.53017 Occurrence Handle1059755
GD Ludden M Okumura K Yano (1977) ArticleTitleAnti-invariant submanifolds of almost contact metric manifolds Math Ann 225 253–261 Occurrence Handle10.1007/BF01425241 Occurrence Handle425821
Murathan C, Arslan K, Ezentaş R (2007) Ricci generalized pseudo-parallel hypersurfaces in real space forms, in print
Murathan C, Arslan K, Ezentaş R (2005) Ricci generalized pseudo-parallel immersions. In: Bures J et al. (eds) Differential Geometry and Its Applications. DGA Proceedings, Prague, pp 99–108
K Nomizu (1968) ArticleTitleOn hypersurfaces satisfying a certain condition on the curvature tensor Tohoku Math J 20 46–59 Occurrence Handle0174.53301 Occurrence Handle226549
ZI Szabó (1982) ArticleTitleStructure theorems on Riemannian manifolds satisfying R(X, Y) · R = 0, I, Local version J Diff Geometry 17 531–582 Occurrence Handle0508.53025
ZI Szabó (1985) ArticleTitleStructure theorems on Riemannian manifolds satisfying R(X, Y) · R = 0, II, Global version Geom Dedicata 19 65–108 Occurrence Handle0612.53023 Occurrence Handle10.1007/BF00233102 Occurrence Handle797152
H Takagi (1972) ArticleTitleAn example of a Riemannian manifold satisfying R(X, Y) · R = 0 but not (∇R = 0) Tohoku Math J 24 105–108 Occurrence Handle0237.53041 Occurrence Handle319109
S Yamaguchi M Kon T Ikawa (1976) ArticleTitle C-Totally real submanifolds J Diff Geometry 11 59–64 Occurrence Handle0329.53039 Occurrence Handle405294
K Yano M Kon (1976) ArticleTitleAnti-invariant submanifolds of a Sasakian space forms, I Tohoku Math J 29 9–23 Occurrence Handle433356
K Yano M Kon (1978) Anti-invariant Submanifolds Dekker New York
K Yano M Kon (1984) Structures on Manifolds World Scientific Singapore Occurrence Handle0557.53001
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Yıldız, A., Murathan, C., Arslan, K. et al. C-Totally real pseudo-parallel submanifolds of Sasakian space forms. Mh Math 151, 247–256 (2007). https://doi.org/10.1007/s00605-007-0474-4
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00605-007-0474-4