• Title/Summary/Keyword: Riemannian

Search Result 543, Processing Time 0.024 seconds

ALMOST EINSTEIN MANIFOLDS WITH CIRCULANT STRUCTURES

  • Dokuzova, Iva
    • Journal of the Korean Mathematical Society
    • /
    • v.54 no.5
    • /
    • pp.1441-1456
    • /
    • 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.

UNIQUENESS OF SOLUTIONS OF A CERTAIN NONLINEAR ELLIPTIC EQUATION ON RIEMANNIAN MANIFOLDS

  • Lee, Yong Hah
    • Bulletin of the Korean Mathematical Society
    • /
    • v.55 no.5
    • /
    • pp.1577-1586
    • /
    • 2018
  • In this paper, we prove that if every bounded ${\mathcal{A}}$-harmonic function on a complete Riemannian manifold M is asymptotically constant at infinity of p-nonparabolic ends of M, then each bounded ${\mathcal{A}}$-harmonic function is uniquely determined by the values at infinity of p-nonparabolic ends of M, where ${\mathcal{A}}$ is a nonlinear elliptic operator of type p on M. Furthermore, in this case, every bounded ${\mathcal{A}}$-harmonic function on M has finite energy.

On the f-biharmonic Maps and Submanifolds

  • Zegga, Kaddour;Cherif, A. Mohamed;Djaa, Mustapha
    • Kyungpook Mathematical Journal
    • /
    • v.55 no.1
    • /
    • pp.157-168
    • /
    • 2015
  • In this paper, we prove that every f-biharmonic map from a complete Riemannian manifold into a Riemannian manifold with non-positive sectional curvature,satisfying some condition, is f-harmonic. Also we present some properties for the f-biharmonicity of submanifolds of $\mathbb{S}^n$, and we give the classification of f-biharmonic curves in 3-dimensional sphere.

ZERMELO'S NAVIGATION PROBLEM ON HERMITIAN MANIFOLDS

  • Lee, Nany
    • Korean Journal of Mathematics
    • /
    • v.14 no.1
    • /
    • pp.79-83
    • /
    • 2006
  • In this paper, we apply Zermelo's problem of navigation on Riemannian manifolds to Hermitian manifolds. Using a similar technique with which we define a Randers metric in a Finsler manifold by perturbing Riemannian metric with a vector field, we construct an $(a,b,f)$-metric in a Rizza manifold from a Hermitian metric and a given vector field.

  • PDF

NIJENHUIS TENSOR FUNCTIONAL ON A SUBSPACE OF METRICS

  • Kang, Bong-Koo
    • The Pure and Applied Mathematics
    • /
    • v.1 no.1
    • /
    • pp.13-18
    • /
    • 1994
  • The study of the integral of the scalar curvature, $A(g)\;=\;{\int}_M\;RdV_9$ as a functional on the set M of all Riemannian metrics of the same total volume on a compact orient able manifold M is now classical, dating back to Hilbert [6] (see also Nagano [8]). Riemannian metric g is a critical point of A(g) if and only if g is an Einstein metric.(omitted)

  • PDF

HARMONIC MAPS BETWEEN THE GROUP OF AUTOMORPHISMS OF THE QUATERNION ALGEBRA

  • Kim, Pu-Young;Park, Joon-Sik;Pyo, Yong-Soo
    • Journal of the Chungcheong Mathematical Society
    • /
    • v.25 no.2
    • /
    • pp.331-339
    • /
    • 2012
  • In this paper, let Q be the real quaternion algebra which consists of all quaternionic numbers, and let G be the Lie group of all automorphisms of the algebra Q. Assume that g is an arbitrary given left invariant Riemannian metric on the Lie group G. Then, we obtain a necessary and sufficient condition for an automorphism of the group G to be harmonic.

NON-EXISTENCE FOR SCREEN QUASI-CONFORMAL IRROTATIONAL HALF LIGHTLIKE SUBMANIFOLDS OF A SEMI-RIEMANNIAN SPACE FORM ADMITTING A SEMI-SYMMETRIC NON-METRIC CONNECTION

  • Jin, Dae Ho
    • East Asian mathematical journal
    • /
    • v.31 no.3
    • /
    • pp.337-344
    • /
    • 2015
  • We study screen quasi-conformal irrotational half lightlike submanifolds M of a semi-Riemannian space form $\bar{M}$ (c) equipped with a semi-symmetric non-metric connection subject such that the structure vector field of $\bar{M}$ (c) belongs to the screen distribution S(TM). The main result is a non-existence theorem for such half lightlike submanifolds.

Geometry of Energy and Bienergy Variations between Riemannian Manifolds

  • CHERIF, AHMED MOHAMED;DJAA, MUSTAPHA
    • Kyungpook Mathematical Journal
    • /
    • v.55 no.3
    • /
    • pp.715-730
    • /
    • 2015
  • In this note, we extend the definition of harmonic and biharmonic maps via the variation of energy and bienergy between two Riemannian manifolds. In particular we present some new properties for the generalized stress energy tensor and the divergence of the generalized stress bienergy.

CONHARMONICALLY FLAT FIBRED RIEMANNIAN SPACE II

  • Lee, Sang-Deok;Kim, Byung-Hak
    • Journal of applied mathematics & informatics
    • /
    • v.9 no.1
    • /
    • pp.441-447
    • /
    • 2002
  • We show that the conharmonical1y flat K-contact find cosymplectic manifolds are local1y Euclidean. Evidently non locally Euclidean conharmonically flat Sasakian manifold does not exist. Moreover we see that conharmonically flat Kenmotsu manifold does not exist and conharmonically flat fibred quasi quasi Sasakian space is locally Euclidean if and only if the scalar curvature of each fibre vanishes identically.

GRADIENT ESTIMATE OF HEAT EQUATION FOR HARMONIC MAP ON NONCOMPACT MANIFOLDS

  • Kim, Hyun-Jung
    • Journal of applied mathematics & informatics
    • /
    • v.28 no.5_6
    • /
    • pp.1461-1466
    • /
    • 2010
  • aSuppose that (M, g) is a complete Riemannian manifold with Ricci curvature bounded below by -K < 0 and (N, $\bar{b}$) is a complete Riemannian manifold with sectional curvature bounded above by a constant $\mu$ > 0. Let u : $M{\times}[0,\;{\infty}]{\rightarrow}B_{\tau}(p)$ is a heat equation for harmonic map. We estimate the energy density of u.