• Title, Summary, Keyword: quasi-projective

Search Result 20, Processing Time 0.037 seconds

ON CONFORMAL AND QUASI-CONFORMAL CURVATURE TENSORS OF AN N(κ)-QUASI EINSTEIN MANIFOLD

  • Hosseinzadeh, Aliakbar;Taleshian, Abolfazl
    • Communications of the Korean Mathematical Society
    • /
    • v.27 no.2
    • /
    • pp.317-326
    • /
    • 2012
  • We consider $N(k)$-quasi Einstein manifolds satisfying the conditions $C({\xi},\;X).S=0$, $\tilde{C}({\xi},\;X).S=0$, $\bar{P}({\xi},\;X).C=0$, $P({\xi},\;X).\tilde{C}=0$ and $\bar{P}({\xi},\;X).\tilde{C}=0$ where $C$, $\tilde{C}$, $P$ and $\bar{P}$ denote the conformal curvature tensor, the quasi-conformal curvature tensor, the projective curvature tensor and the pseudo projective curvature tensor, respectively.

CERTAIN DISCRIMINATIONS OF PRIME ENDOMORPHISM AND PRIME MATRIX

  • Bae, Soon-Sook
    • East Asian mathematical journal
    • /
    • v.14 no.2
    • /
    • pp.259-268
    • /
    • 1998
  • In this paper, for a commutative ring R with an identity, considering the endomorphism ring $End_R$(M) of left R-module $_RM$ which is (quasi-)injective or (quasi-)projective, some discriminations of prime endomorphism were found as follows: each epimorphism with the irreducible(or simple) kernel on a (quasi-)injective module and each monomorphism with maximal image on a (quasi-)projective module are prime. It was shown that for a field F, any given square matrix in $Mat_{n{\times}n}$(F) with maximal image and irreducible kernel is a prime matrix, furthermore, any given matrix in $Mat_{n{\times}n}$(F) for any field F can be factored into a product of prime matrices.

  • PDF

𝒵 Tensor on N(k)-Quasi-Einstein Manifolds

  • Mallick, Sahanous;De, Uday Chand
    • Kyungpook Mathematical Journal
    • /
    • v.56 no.3
    • /
    • pp.979-991
    • /
    • 2016
  • The object of the present paper is to study N(k)-quasi-Einstein manifolds. We study an N(k)-quasi-Einstein manifold satisfying the curvature conditions $R({\xi},X){\cdot}Z=0$, $Z(X,{\xi}){\cdot}R=0$, and $P({\xi},X){\cdot}Z=0$, where R, P and Z denote the Riemannian curvature tensor, the projective curvature tensor and Z tensor respectively. Next we prove that the curvature condition $C{\cdot}Z=0$ holds in an N(k)-quasi-Einstein manifold, where C is the conformal curvature tensor. We also study Z-recurrent N(k)-quasi-Einstein manifolds. Finally, we construct an example of an N(k)-quasi-Einstein manifold and mention some physical examples.

MINIMAL QUASI-F COVERS OF REALCOMPACT SPACES

  • Jeon, Young Ju;Kim, Chang Il
    • The Pure and Applied Mathematics
    • /
    • v.23 no.4
    • /
    • pp.329-337
    • /
    • 2016
  • In this paper, we show that every compactification, which is a quasi-F space, of a space X is a Wallman compactification and that for any compactification K of the space X, the minimal quasi-F cover QFK of K is also a Wallman compactification of the inverse image ${\Phi}_K^{-1}(X)$ of the space X under the covering map ${\Phi}_K:QFK{\rightarrow}K$. Using these, we show that for any space X, ${\beta}QFX=QF{\beta}{\upsilon}X$ and that a realcompact space X is a projective object in the category $Rcomp_{\sharp}$ of all realcompact spaces and their $z^{\sharp}$-irreducible maps if and only if X is a quasi-F space.

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

  • Baishya, Kanak Kanti;Chowdhury, Partha Roy
    • Communications of the Korean Mathematical Society
    • /
    • v.31 no.1
    • /
    • pp.163-176
    • /
    • 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.

Curvature Properties of 𝜂-Ricci Solitons on Para-Kenmotsu Manifolds

  • Singh, Abhishek;Kishor, Shyam
    • Kyungpook Mathematical Journal
    • /
    • v.59 no.1
    • /
    • pp.149-161
    • /
    • 2019
  • In the present paper, we study curvature properties of ${\eta}$-Ricci solitons on para-Kenmotsu manifolds. We obtain some results of ${\eta}$-Ricci solitons on para-Kenmotsu manifolds satisfying $R({\xi},X).C=0$, $R({\xi},X).{\tilde{M}}=0$, $R({\xi},X).P=0$, $R({\xi},X).{\tilde{C}}=0$ and $R({\xi},X).H=0$, where $C,\;{\tilde{M}},\;P,\;{\tilde{C}}$ and H are a quasi-conformal curvature tensor, a M-projective curvature tensor, a pseudo-projective curvature tensor, and a concircular curvature tensor and conharmonic curvature tensor, respectively.

ALGEBRAIC POINTS ON THE PROJECTIVE LINE

  • Ih, Su-Ion
    • Journal of the Korean Mathematical Society
    • /
    • v.45 no.6
    • /
    • pp.1635-1646
    • /
    • 2008
  • Schanuel's formula describes the distribution of rational points on projective space. In this paper we will extend it to algebraic points of bounded degree in the case of ${\mathbb{P}}^1$. The estimate formula will also give an explicit error term which is quite small relative to the leading term. It will also lead to a quasi-asymptotic formula for the number of points of bounded degree on ${\mathbb{P}}^1$ according as the height bound goes to $\infty$.