• Title/Summary/Keyword: Sasakian structure

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A NEW TYPE WARPED PRODUCT METRIC IN CONTACT GEOMETRY

  • Mollaogullari, Ahmet;Camci, Cetin
    • Honam Mathematical Journal
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    • v.44 no.1
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    • pp.62-77
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    • 2022
  • This study presents an 𝛼-Sasakian structure on the product manifold M1 × 𝛽(I), where M1 is a Kähler manifold with an exact 1-form, and 𝛽(I) is an open curve. It then defines a new type warped product metric to study the warped product of almost Hermitian manifolds with almost contact metric manifolds, contact metric manifolds, and K-contact manifolds.

SCALAR CURVATURE OF CONTACT THREE CR-SUBMANIFOLDS IN A UNIT (4m + 3)-SPHERE

  • Kim, Hyang-Sook;Pak, Jin-Suk
    • Bulletin of the Korean Mathematical Society
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    • v.48 no.3
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    • pp.585-600
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    • 2011
  • In this paper we derive an integral formula on an (n + 3)-dimensional, compact, minimal contact three CR-submanifold M of (p-1) contact three CR-dimension immersed in a unit (4m+3)-sphere $S^{4m+3}$. Using this integral formula, we give a sufficient condition concerning the scalar curvature of M in order that such a submanifold M is to be a generalized Clifford torus.

THE k-ALMOST RICCI SOLITONS AND CONTACT GEOMETRY

  • Ghosh, Amalendu;Patra, Dhriti Sundar
    • Journal of the Korean Mathematical Society
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    • v.55 no.1
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    • pp.161-174
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    • 2018
  • The aim of this article is to study the k-almost Ricci soliton and k-almost gradient Ricci soliton on contact metric manifold. First, we prove that if a compact K-contact metric is a k-almost gradient Ricci soliton, then it is isometric to a unit sphere $S^{2n+1}$. Next, we extend this result on a compact k-almost Ricci soliton when the flow vector field X is contact. Finally, we study some special types of k-almost Ricci solitons where the potential vector field X is point wise collinear with the Reeb vector field ${\xi}$ of the contact metric structure.