KaydedilenlerDerginizi ekleyin

Dergiler / Turkish Journal of Mathematics / 2015 / Cilt: 39 - Sayı: 4

Warped product skew semi-invariantsubmanifolds of order $1$ of a locallyproduct Riemannian manifold

Hakan Mete TAŞTAN
Sayfa
453–466
Yayın Tarihi
2015-08-13
DOI
—
🏛️Bu makalenin bibliyografik verileri ve tam metin bağlantısı DergiPark üzerinden sağlanmıştır.
DergiPark Kaydı ↗
✨

Yapay Zeka Hızlı Bakış & Çıkarımlar

AI Insight
⚡ TL;DR(1 Cümlede Hızlı Çıkarım)

The equality case is also discussed.

📌 3 Maddede Bu Makale

🎯
Amaç & Hipotez:We introduce warped product skew semi-invariant submanifolds of order $1$ of a locally product Riemannian manifold.
📊
Temel Bulgular & Veri:We give a necessary and sufficient condition for a skew semi-invariant submanifold of order 1 to be a locally warped product.
💡
Sonuç & Katkı:The equality case is also discussed.
🔬Tür:Araştırma Makalesi
📍Kapsam:Genişletilmiş Akademik Örneklem
⚙️Değişkenler:Locally product manifold · warped product submanifold · skew semi-invariant submanifold

Özet

We introduce warped product skew semi-invariant submanifolds of order $1$ of a locally product Riemannian manifold. We give a necessary and sufficient condition for a skew semi-invariant submanifold of order 1 to be a locally warped product. We also establish an inequality between the warping function and the squared norm of the second fundamental form for such submanifolds. The equality case is also discussed.

Abstract

We introduce warped product skew semi-invariant submanifolds of order $1$ of a locally product Riemannian manifold. We give a necessary and sufficient condition for a skew semi-invariant submanifold of order 1 to be a locally warped product. We also establish an inequality between the warping function and the squared norm of the second fundamental form for such submanifolds. The equality case is also discussed.

🔖

Bu Makaleye Atıf Yap

TAŞTAN, H. M. (2015). Warped product skew semi-invariantsubmanifolds of order $1$ of a locallyproduct Riemannian manifold. Turkish Journal of Mathematics, Cilt: 39 - Sayı: 4, 453–466. https://ajindex.com/articles/723302

📄 Tam Metin PDF Okuyucu

📄

PDF görüntüleyici hazırlanıyor...

Kaynakça (7)

  1. Al-Solamy FR, Khan MA. Warped product submanifolds of Riemannian product manifolds. Abstract and Applied Analysis 2012; Article ID 724898, 12 pages, doi:10.1155/2012/724898. Arslan K, Carriazo A, Chen BY, Murathan C. On slant submanifolds of neutral Kaehler manifolds. Taiwanese J Math 2010; 17: 561–584. At¸ceken M. Warped product semi-slant submanifolds in locally Riemannian product manifolds. Bull Austral Math Soc 2008; 77: 177–186. Bejancu A. CR-Submanifolds of Kaehler manifold I. Proc Amer Math Soc 1978; 69: 135–142. Bejancu A. Semi-invariant submanifolds of locally product Riemannian manifolds. An Univ Timi¸soara Ser S¸tiint Math Al 1984; 22: 3–11.
  2. Bishop RL, O’Neill B. Manifolds of negative curvature. Trans Amer Math Soc 1969; 145: 1–49.
  3. Cabrerizo JL, Carriazo A, Fern´andez LM, Fern´andez M. Slant submanifolds in Sasakian manifolds. Glasgow Math J 2000; 42: 125–138. Carriazo A. Bi-slant immersions. In: Proc ICRAMS 2000,
  4. Kharagpur, India, 2000, 88–97. Chen BY. Slant immersions. Bull Austral Math Soc 1990; 41: 135–147. Chen BY. Geometry of warped product in Kaehler manifolds. Monatsh Math 2001; 133: 177–195. Chen BY. Geometry of warped product submanifolds: a survey. J Adv Math Stud 2013; 6: 1–43.
  5. Dillen F, N¨olker S. Semi-paralellity multi rotation surfaces and the helix property. J Reine Angew Math 1993; 435: 33– Hiepko S. Eine innere Kennzeichnung der verzertten Produkte. Math Ann 1979; 241: 209–215 (in German). Khan VA, Khan MA. Pseudo-slant submanifolds of a Sasakian manifold. Indian J Pure Appl Math 2007; 38: 31–42.
  6. Khursheed Haider SM, Thakur M, Advin M. Warped product skew CR-submanifolds of a Cosymplectic manifold. Lobachevskii J Math 2012; 33: 262–273.
  7. Liu X, Shao FM. Skew semi-invariant submanifolds of a locally product manifold. Portugaliae Math 1999; 56: 319–327. Lotta A. Slant submanifolds in contact geometry. Bull Math Soc Sci 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. 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 semi-invariant submanifolds of a locally product Riemannian manifold. Bull Math Soc Sci Roumanie 2006; 49: 383–394. S¸ahin B. Warped product semi-slant submanifolds of a locally product Riemannian manifold. Studia Sci Math Hungarica 2009;