• Title/Summary/Keyword: Conformal

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CONFORMAL HEMI-SLANT SUBMERSION FROM KENMOTSU MANIFOLD

  • Mohammad Shuaib;Tanveer Fatima
    • Honam Mathematical Journal
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    • v.45 no.2
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    • pp.248-268
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    • 2023
  • As a generalization of conformal semi-invariant submersion, conformal slant submersion and conformal semi-slant submersion, in this paper we study conformal hemi-slant submersion from Kenmotsu manifold onto a Riemannian manifold. The necessary and sufficient conditions for the integrability and totally geodesicness of distributions are discussed. Moreover, we have obtained sufficient condition for a conformal hemi-slant submersion to be a homothetic map. The condition for a total manifold of the submersion to be twisted product is studied, followed by other decomposition theorems.

LOCALLY CONFORMAL KÄHLER MANIFOLDS AND CONFORMAL SCALAR CURVATURE

  • Kim, Jae-Man
    • Communications of the Korean Mathematical Society
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    • v.25 no.2
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    • pp.245-249
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    • 2010
  • We show that on a compact locally conformal K$\ddot{a}$hler manifold $M^{2n}$ (dim $M^{2n}\;=\;2n\;{\geq}\;4$), $M^{2n}$ is K$\ddot{a}$hler if and only if its conformal scalar curvature k is not smaller than the scalar curvature s of $M^{2n}$ everywhere. As a consequence, if a compact locally conformal K$\ddot{a}$hler manifold $M^{2n}$ is both conformally flat and scalar flat, then $M^{2n}$ is K$\ddot{a}$hler. In contrast with the compact case, we show that there exists a locally conformal K$\ddot{a}$hler manifold with k equal to s, which is not K$\ddot{a}$hler.

EINSTEIN HALF LIGHTLIKE SUBMANIFOLDS WITH SPECIAL CONFORMALITIES

  • Jin, Dae Ho
    • Bulletin of the Korean Mathematical Society
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    • v.49 no.6
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    • pp.1163-1178
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    • 2012
  • In this paper, we study the geometry of Einstein half lightlike submanifolds M of a semi-Riemannian space form $\bar{M}(c)$ subject to the conditions: (a) M is screen conformal, and (b) the coscreen distribution of M is a conformal Killing one. The main result is a classification theorem for screen conformal Einstein half lightlike submanifolds of a Lorentzian space form with a conformal Killing coscreen distribution.

Finslerian Hypersurface and Generalized β-Conformal Change of Finsler Metric

  • Tiwari, Shiv Kumar;Rai, Anamika
    • Kyungpook Mathematical Journal
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    • v.58 no.4
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    • pp.781-788
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    • 2018
  • In the present paper, we have studied the Finslerian hypersurfaces and generalized ${\beta}$-conformal change of Finsler metric. The relations between the Finslerian hypersurface and the other which is Finslerian hypersurface given by generalized ${\beta}$-conformal change have been obtained. We have also proved that generalized ${\beta}$-conformal change makes three types of hypersurfaces invariant under certain conditions.

CONFORMAL HEMI-SLANT SUBMERSIONS FROM ALMOST HERMITIAN MANIFOLDS

  • Kumar, Sumeet;Kumar, Sushil;Pandey, Shashikant;Prasad, Rajendra
    • Communications of the Korean Mathematical Society
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    • v.35 no.3
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    • pp.999-1018
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    • 2020
  • In this paper, our main objective is to introduce the notion of conformal hemi-slant submersions from almost Hermitian manifolds onto Riemannian manifolds as a generalized case of conformal anti-invariant submersions, conformal semi-invariant submersions and conformal slant submersions. We mainly focus on conformal hemi-slant submersions from Kähler manifolds. During this manner, we tend to study and investigate integrability of the distributions which are arisen from the definition of the submersions and the geometry of leaves of such distributions. Moreover, we tend to get necessary and sufficient conditions for these submersions to be totally geodesic for such manifolds. We also provide some quality examples of conformal hemi-slant submersions.

CONFORMAL CHANGES OF A RIZZA MANIFOLD WITH A GENERALIZED FINSLER STRUCTURE

  • Park, Hong-Suh;Lee, Il-Yong
    • Bulletin of the Korean Mathematical Society
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    • v.40 no.2
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    • pp.327-340
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    • 2003
  • We are devoted to dealing with the conformal theory of a Rizza manifold with a generalized Finsler metric $G_{ij}$ (x,y) and a new conformal invariant non-linear connection $M^{i}$ $_{j}$ (x,y) constructed from the generalized Cern's non-linear connection $N^{i}$ $_{j}$ (x,y) and almost complex structure $f^{i}$ $_{j}$ (x). First, we find a conformal invariant connection ( $M_{j}$ $^{i}$ $_{k}$ , $M^{i}$ $_{j}$ , $C_{j}$ $^{i}$ $_{k}$ ) and conformal invariant tensors. Next, the nearly Kaehlerian (G, M)-structures under conformal change in a Rizza manifold are investigate.

CONFORMAL HEMI-SLANT SUBMERSIONS FROM COSYMPLECTIC MANIFOLDS

  • Vinay Kumar;Rajendra Prasad;Sandeep Kumar Verma
    • Communications of the Korean Mathematical Society
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    • v.38 no.1
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    • pp.205-221
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    • 2023
  • The main goal of the paper is the introduction of the notion of conformal hemi-slant submersions from almost contact metric manifolds onto Riemannian manifolds. It is a generalization of conformal anti-invariant submersions, conformal semi-invariant submersions and conformal slant submersions. Our main focus is conformal hemi-slant submersion from cosymplectic manifolds. We tend also study the integrability of the distributions involved in the definition of the submersions and the geometry of their leaves. Moreover, we get necessary and sufficient conditions for these submersions to be totally geodesic, and provide some representative examples of conformal hemi-slant submersions.

ON GENERALIZED QUASI-CONFORMAL N(k, μ)-MANIFOLDS

  • Baishya, Kanak Kanti;Chowdhury, Partha Roy
    • Communications of the Korean Mathematical Society
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    • v.31 no.1
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    • pp.163-176
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    • 2016
  • The object of the present paper is to introduce a new curvature tensor, named generalized quasi-conformal curvature tensor which bridges conformal curvature tensor, concircular curvature tensor, projective curvature tensor and conharmonic curvature tensor. Flatness and symmetric properties of generalized quasi-conformal curvature tensor are studied in the frame of (k, ${\mu}$)-contact metric manifolds.

EINSTEIN SPACES AND CONFORMAL VECTOR FIELDS

  • KIM DONG-SOO;KIM YOUNG HO;PARK SEONG-HEE
    • Journal of the Korean Mathematical Society
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    • v.43 no.1
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    • pp.133-145
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    • 2006
  • We study Riemannian or pseudo-Riemannian manifolds which admit a closed conformal vector field. Subject to the condition that at each point $p{\in}M^n$ the set of conformal gradient vector fields spans a non-degenerate subspace of TpM, using a warped product structure theorem we give a complete description of the space of conformal vector fields on arbitrary non-Ricci flat Einstein spaces.