• Title/Summary/Keyword: Riemannian manifolds

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VANISHING PROPERTIES OF p-HARMONIC ℓ-FORMS ON RIEMANNIAN MANIFOLDS

  • Nguyen, Thac Dung;Pham, Trong Tien
    • Journal of the Korean Mathematical Society
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    • v.55 no.5
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    • pp.1103-1129
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    • 2018
  • In this paper, we show several vanishing type theorems for p-harmonic ${\ell}$-forms on Riemannian manifolds ($p{\geq}2$). First of all, we consider complete non-compact immersed submanifolds $M^n$ of $N^{n+m}$ with flat normal bundle, we prove that any p-harmonic ${\ell}$-form on M is trivial if N has pure curvature tensor and M satisfies some geometric conditions. Then, we obtain a vanishing theorem on Riemannian manifolds with a weighted $Poincar{\acute{e}}$ inequality. Final, we investigate complete simply connected, locally conformally flat Riemannian manifolds M and point out that there is no nontrivial p-harmonic ${\ell}$-form on M provided that the Ricci curvature has suitable bound.

ALMOST EINSTEIN MANIFOLDS WITH CIRCULANT STRUCTURES

  • Dokuzova, Iva
    • Journal of the Korean Mathematical Society
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    • v.54 no.5
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    • pp.1441-1456
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    • 2017
  • We consider a 3-dimensional Riemannian manifold M with a circulant metric g and a circulant structure q satisfying $q^3=id$. The structure q is compatible with g such that an isometry is induced in any tangent space of M. We introduce three classes of such manifolds. Two of them are determined by special properties of the curvature tensor. The third class is composed by manifolds whose structure q is parallel with respect to the Levi-Civita connection of g. We obtain some curvature properties of these manifolds (M, g, q) and give some explicit examples of such manifolds.

SOME TYPES OF SLANT SUBMANIFOLDS OF BRONZE RIEMANNIAN MANIFOLDS

  • Acet, Bilal Eftal;Acet, Tuba
    • The Pure and Applied Mathematics
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    • v.29 no.4
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    • pp.277-291
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    • 2022
  • The aim of this article is to examine some types of slant submanifolds of bronze Riemannian manifolds. We introduce hemi-slant submanifolds of a bronze Riemannian manifold. We obtain integrability conditions for the distribution involved in quasi hemi-slant submanifold of a bronze Riemannian manifold. Also, we give some examples about this type submanifolds.

GENERALIZED CHEN INEQUALITY FOR CR-WARPED PRODUCTS OF LOCALLY CONFORMAL KÄHLER MANIFOLDS

  • Harmandeep Kaur;Gauree Shanker;Ramandeep Kaur;Abdulqader Mustafa
    • Honam Mathematical Journal
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    • v.46 no.1
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    • pp.47-59
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    • 2024
  • The purpose of the Nash embedding theorem was to take extrinsic help for studying the intrinsic Riemannian geometry. To realize this aim in actual practice there is a need for optimal relationships between the known intrinsic invariants and the main extrinsic invariants for Riemannian submanifolds. This paper aims to provide an optimal relationship for CR-warped product submanifolds of locally conformal Kähler manifolds.

RIGIDITY OF COMPLETE RIEMANNIAN MANIFOLDS WITH VANISHING BACH TENSOR

  • Huang, Guangyue;Ma, Bingqing
    • Bulletin of the Korean Mathematical Society
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    • v.56 no.5
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    • pp.1341-1353
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    • 2019
  • For complete Riemannian manifolds with vanishing Bach tensor and positive constant scalar curvature, we provide a rigidity theorem characterized by some pointwise inequalities. Furthermore, we prove some rigidity results under an inequality involving $L^{\frac{n}{2}}$-norm of the Weyl curvature, the traceless Ricci curvature and the Sobolev constant.

AN IMPROVED UNIFYING CONVERGENCE ANALYSIS OF NEWTON'S METHOD IN RIEMANNIAN MANIFOLDS

  • Argyros, Ioannis K.
    • Journal of applied mathematics & informatics
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    • v.25 no.1_2
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    • pp.345-351
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    • 2007
  • Using more precise majorizing sequences we provide a finer convergence analysis than before [1], [7] of Newton's method in Riemannian manifolds with the following advantages: weaker hypotheses, finer error bounds on the distances involved and a more precise information on the location of the singularity of the vector field.