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Dergiler / Turkish Journal of Mathematics / 2015 / Cilt: 39 - Sayı: 2

The geometry of hemi-slant submanifolds of a locally product Riemannian manifold

Hakan Mete TAŞTAN
Fatma ÖZDEMİR
Sayfa
268–284
Yayın Tarihi
2015-03-15
DOI
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⚡ TL;DR(1 Cümlede Hızlı Çıkarım)

Finally, we obtain a basic inequality involving Ricci curvature and the squared mean curvature of a hemi-slant submanifold of a certain type of locally product Riemannian manifolds.

📌 3 Maddede Bu Makale

🎯
Amaç & Hipotez:In the present paper, we study hemi-slant submanifolds of a locally product Riemannian manifold.
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Temel Bulgular & Veri:We prove that the anti-invariant distribution involved in the definition of hemi-slant submanifold is integrable and give some applications of this result.
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Sonuç & Katkı:Finally, we obtain a basic inequality involving Ricci curvature and the squared mean curvature of a hemi-slant submanifold of a certain type of locally product Riemannian manifolds.
🔬Tür:Araştırma Makalesi
📍Kapsam:Genişletilmiş Akademik Örneklem
⚙️Değişkenler:Locally product manifold · hemi-slant submanifold · slant distribution

Özet

In the present paper, we study hemi-slant submanifolds of a locally product Riemannian manifold. We prove that the anti-invariant distribution involved in the definition of hemi-slant submanifold is integrable and give some applications of this result. We get a necessary and sufficient condition for a proper hemi-slant submanifold to be a hemi-slant product. We also study these types of submanifolds with parallel canonical structures. Moreover, we give two characterization theorems for the totally umbilical proper hemi-slant submanifolds. Finally, we obtain a basic inequality involving Ricci curvature and the squared mean curvature of a hemi-slant submanifold of a certain type of locally product Riemannian manifolds.

Abstract

In the present paper, we study hemi-slant submanifolds of a locally product Riemannian manifold. We prove that the anti-invariant distribution involved in the definition of hemi-slant submanifold is integrable and give some applications of this result. We get a necessary and sufficient condition for a proper hemi-slant submanifold to be a hemi-slant product. We also study these types of submanifolds with parallel canonical structures. Moreover, we give two characterization theorems for the totally umbilical proper hemi-slant submanifolds. Finally, we obtain a basic inequality involving Ricci curvature and the squared mean curvature of a hemi-slant submanifold of a certain type of locally product Riemannian manifolds.

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Bu Makaleye Atıf Yap

TAŞTAN, H. M., ÖZDEMİR, F. (2015). The geometry of hemi-slant submanifolds of a locally product Riemannian manifold. Turkish Journal of Mathematics, Cilt: 39 - Sayı: 2, 268–284. https://ajindex.com/articles/185715

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Kaynakça (8)

  1. Adati T. Submanifolds of an almost product manifold. Kodai Math J 1981; 4: 327–343. Alegre P. Slant submanifolds of Lorentzian Sasakian and Para-Sasakian manifolds. Taiwanese J Math 2013; 17: 897–910. DOI:10.11650/tjm.17.2013.2427. Al-Solamy FR, Khan MA, Uddin S. Totally umbilical hemi-slant submanifolds of K¨ahler manifolds. Abstr Appl Anal 2011; Art. ID 987157, 9 pp. Arslan K, Carriazo A, Chen BY, Murathan C. On slant submanifolds of neutral Kaehler manifolds. Taiwanese J Math 2010; 17: 561–584. Bejancu A. Semi-invariant submanifolds of locally product Riemannian manifolds. An Univ Timi¸soara Ser S¸tiint Math Al 1984; 22: 3–11.
  2. Cabrerizo JL, Carriazo A, Fernandez LM, Fernandez M. Slant submanifolds in Sasakian manifolds. Glasgow Math J 2000; 42: 125–138. Carriazo A. Bi-slant immersions. In: Proc. ICRAMS 2000,
  3. Kharagpur, India, 2000, 88–97. Chen BY. Geometry of slant submanifolds. Katholieke Universiteit Leuven, 1990. Chen BY. Relations between Ricci curvature and shape operator for submanifolds with arbitrary codimensions. Glasgow Math J 1999; 41: 33–41.
  4. Hong S, Tripathi MM. On Ricci curvature of submanifolds. Internat J Pure Appl Math Sci 2005; 2: 227–246.
  5. Khan VA, Khan MA. Pseudo-slant submanifolds of a Sasakian manifold. Indian J Pure Appl Math 2007; 38: 31–42.
  6. Li H, Liu X. Semi-slant submanifolds of a locally product manifold. Georgian Math J 2005; 12: 273–282. Lotta A. Slant submanifolds in contact geometry. Bull Math Soc Roumanie 1996; 39: 183–198. Papaghiuc N. Semi-slant submanifolds of a K¨ahlerian manifold. Ann S¸t Al I Cuza Univ Ia¸si 1994; 40: 55–61. Pitis G. On some submanifolds of a locally product manifold. Kodai Math J 1986; 9: 327–333. Ronsse GS. Generic and skew CR-submanifolds of a K¨ahler manifold. Bull Inst Math Acad Sinica 1990; 18: 127–141. S¸ahin B. Slant submanifolds of an almost product Riemannian manifold. J Korean Math Soc 2006; 43: 717–732. S ¸ahin B. Warped product submanifolds of a K¨ ahler manifold with a slant factor. Ann Pol Math 2009; 95: 207–226. Ta¸stan HM. The axiom of hemi-slant 3-spheres in almost Hermitian geometry. Bull Malays Math Sci Soc(2) 2014; 37: 555–564. Tripathi MM. Generic submanifolds of generalized complex space forms. Publ Math Debrecen 1997; 50: 373–392.
  7. Uddin S, Khan MA, Singh K. A note on totally umbilical pseudo-slant submanifolds of a nearly K¨ahler manifold. Acta Univ Apulensis Math Inform 2012; 29: 279–285.
  8. Yano K, Kon M. Structures on Manifolds. Singapore: World Scientific, 1984.