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Journals / Turkish Journal of Mathematics / 2014 / Cilt: 38 - Sayı: 4

On semiparallel anti-invariant submanifolds of generalized Sasakian space forms

Cihan ÖZGÜR
Fatma GÜRLER
Cengizhan MURATHAN
Pages
796–802
Publication Date
2022-11-05
DOI
—
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AI Summary & Key Takeaways

AI Insight
⚡ TL;DR(Too Long; Didn't Read)

We show that the submanifolds are totally geodesic under certain conditions.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:We consider minimal anti-invariant semiparallel submanifolds of generalized Sasakian space forms.
📊
Key Findings & Data:We consider minimal anti-invariant semiparallel submanifolds of generalized Sasakian space forms.
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Conclusion & Impact:We show that the submanifolds are totally geodesic under certain conditions.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Semiparallel submanifold · generalized Sasakian space form · Laplacian of the second fundamental form

Abstract

We consider minimal anti-invariant semiparallel submanifolds of generalized Sasakian space forms. We show that the submanifolds are totally geodesic under certain conditions.

Özet

We consider minimal anti-invariant semiparallel submanifolds of generalized Sasakian space forms. We show that the submanifolds are totally geodesic under certain conditions.

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Cite This Article

ÖZGÜR, C., GÜRLER, F., MURATHAN, C. (2022). On semiparallel anti-invariant submanifolds of generalized Sasakian space forms. Turkish Journal of Mathematics, Cilt: 38 - Sayı: 4, 796–802. https://ajindex.com/articles/608286

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References (8)

  1. Alegre P, Blair DE, Carriazo A. Generalized Sasakian space-forms. Israel J Math 2004; 141: 157–183.
  2. Alegre P, Carriazo A. Submanifolds of generalized Sasakian space forms. Taiwanese J Math 2009; 13: 923–941.
  3. Asperti AC, Mercuri F. Semi-parallel immersions into space forms. Boll Un Mat Ital 1994; 8B: 883–895. Blair DE. Riemannian Geometry of Contact and Symplectic Manifolds. Boston: Birkhauser, 2002.
  4. Brasil A, Lobos GA, Mariano M. C -totally real submanifolds with parallel mean curvature in λ -Sasakian space forms. Mat Contemp 2008; 34: 83–102. Chen BY. Geometry of Submanifolds. Pure and Applied Mathematics. New York: Marcel Dekker, 1973. Deprez J. Semiparallel hypersurfaces. Rend Sem Mat Univ Politec Torino 1986; 44: 303–316. Deprez J. Semi-parallel immersions. In: Morvan JM, Verstraelen L, editors. Geometry and Topology of Submanifolds. Singapore: World Scientific, 1989, pp. 73–88. Dillen F. Semi-parallel hypersurfaces of a real space form. Israel J Math 1991; 75: 193–202.
  5. Janssens D, Vanhecke L. Almost contact structures and curvature tensors. Kodai Math J 1981; 4: 1–27. Kenmotsu K. A class of almost contact Riemannian manifolds. Tohoku Math J 1972; 24: 93–103. Ludden GD. Submanifolds of cosymplectic manifolds. J Differential Geometry 1970; 4: 237–244. ¨ Ozg¨ ur C, Murathan C. On invariant submanifolds of Lorentzian para-Sasakian manifolds. Arab J Sci Eng Sect A Sci 2009; 34: 177–185. Sular S. Kenmotsu manifolds and their some submanifolds. PhD, Balıkesir University, Balıkesir, Turkey, 2009. Sular S, ¨ Ozg¨ ur C, Murathan C. Pseudoparallel anti-invariant submanifolds of Kenmotsu manifolds. Hacettepe J Math Stat 2010; 39: 535–543.
  6. Van der Veken J, Vrancken L. Parallel and semi-parallel hypersurfaces of S n × R. Bull Braz Math Soc (NS) 2008; 39: 355–370.
  7. Yano K, Kon M. Structures on Manifolds. Series in Pure Mathematics. Singapore: World Scientific, 1984.
  8. Yıldız A, Murathan C, Arslan K, Ezenta¸s R. C -totally real pseudo-parallel submanifolds of Sasakian space forms. Monatsh- Math 2007; 151: 247-256.