• Title/Summary/Keyword: warped product metric

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ISOTROPIC MEAN BERWALD FINSLER WARPED PRODUCT METRICS

  • Mehran Gabrani;Bahman Rezaei;Esra Sengelen Sevim
    • Bulletin of the Korean Mathematical Society
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    • v.60 no.6
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    • pp.1641-1650
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    • 2023
  • It is our goal in this study to present the structure of isotropic mean Berwald Finsler warped product metrics. We bring out the rich class of warped product Finsler metrics behaviour under this condition. We show that every Finsler warped product metric of dimension n ≥ 2 is of isotropic mean Berwald curvature if and only if it is a weakly Berwald metric. Also, we prove that every locally dually flat Finsler warped product metric is weakly Berwaldian. Finally, we prove that every Finsler warped product metric is of isotropic Berwald curvature if and only if it is a Berwald metric.

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.

SOME METRIC ON EINSTEIN LORENTZIAN WARPED PRODUCT MANIFOLDS

  • Lee, Soo-Young
    • Korean Journal of Mathematics
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    • v.27 no.4
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    • pp.1133-1147
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    • 2019
  • In this paper, let M = B×f2 F be an Einstein Lorentzian warped product manifold with 2-dimensional base. We study the geodesic completeness of some metric with constant curvature. First of all, we discuss the existence of nonconstant warping functions on M. As the results, we have some metric g admits nonconstant warping functions f. Finally, we consider the geodesic completeness on M.

NONCONSTANT WARPING FUNCTIONS ON EINSTEIN WARPED PRODUCT MANIFOLDS WITH 2-DIMENSIONAL BASE

  • Lee, Soo-Young
    • Korean Journal of Mathematics
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    • v.26 no.1
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    • pp.75-85
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    • 2018
  • In this paper, we study nonconstant warping functions on an Einstein warped product manifold $M=B{\times}_{f^2}F$ with a warped product metric $g=g_B+f(t)^2g_F$. And we consider a 2-dimensional base manifold B with a metric $g_B=dt^2+(f^{\prime}(t))^2du^2$. As a result, we prove the following: if M is an Einstein warped product manifold with a 2-dimensional base, then there exist generally nonconstant warping functions f(t).

NONCONSTANT WARPING FUNCTIONS ON EINSTEIN LORENTZIAN WARPED PRODUCT MANIFOLDS

  • Jung, Yoon-Tae;Choi, Eun-Hee;Lee, Soo-Young
    • Honam Mathematical Journal
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    • v.40 no.3
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    • pp.447-456
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    • 2018
  • In this paper, we consider nonconstant warping functions on Einstein Lorentzian warped product manifolds $M=B{\times}_{f^2}F$ with an 1-dimensional base B which has a negative definite metric. As the results, we discuss that on M the resulting Einstein Lorentzian warped product metric is a future (or past) geodesically complete one outside a compact set.

THE CRITICAL POINT EQUATION ON A FOUR DIMENSIONAL WARPED PRODUCT MANIFOLD

  • Hwang, Seung-Su;Chang, Jeong-Wook
    • Bulletin of the Korean Mathematical Society
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    • v.43 no.4
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    • pp.679-692
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    • 2006
  • On a compact oriented n-dimensional manifold $(M^n,\;g)$, it has been conjectured that a metric g satisfying the critical point equation (2) should be Einstein. In this paper, we prove that if a manifold $(M^4,\;g)$ is a 4-dimensional oriented compact warped product, then g can not be a solution of CPE with a non-zero solution function f.

GEOMETRIC INEQUALITIES FOR WARPED PRODUCTS SUBMANIFOLDS IN GENERALIZED COMPLEX SPACE FORMS

  • Mohd Aquib;Mohd Aslam;Michel Nguiffo Boyom;Mohammad Hasan Shahid
    • Communications of the Korean Mathematical Society
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    • v.38 no.1
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    • pp.179-193
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    • 2023
  • In this article, we derived Chen's inequality for warped product bi-slant submanifolds in generalized complex space forms using semisymmetric metric connections and discuss the equality case of the inequality. Further, we discuss non-existence of such minimal immersion. We also provide various applications of the obtained inequalities.

GENERALIZED m-QUASI-EINSTEIN STRUCTURE IN ALMOST KENMOTSU MANIFOLDS

  • Mohan Khatri;Jay Prakash Singh
    • Bulletin of the Korean Mathematical Society
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    • v.60 no.3
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    • pp.717-732
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    • 2023
  • The goal of this paper is to analyze the generalized m-quasi-Einstein structure in the context of almost Kenmotsu manifolds. Firstly we showed that a complete Kenmotsu manifold admitting a generalized m-quasi-Einstein structure (g, f, m, λ) is locally isometric to a hyperbolic space ℍ2n+1(-1) or a warped product ${\tilde{M}}{\times}{_{\gamma}{\mathbb{R}}$ under certain conditions. Next, we proved that a (κ, µ)'-almost Kenmotsu manifold with h' ≠ 0 admitting a closed generalized m-quasi-Einstein metric is locally isometric to some warped product spaces. Finally, a generalized m-quasi-Einstein metric (g, f, m, λ) in almost Kenmotsu 3-H-manifold is considered and proved that either it is locally isometric to the hyperbolic space ℍ3(-1) or the Riemannian product ℍ2(-4) × ℝ.