Remarks on Scalar Curvature and Concircular Field Equation
نویسندگان
چکیده
We show that the scalar curvature of a Riemannian manifold $M$ is constant if it satisfies (i) concircular field equation and compact, (ii) special equation. Finally, we that, complete connected admits non-isometric vector leaving invariant, conformal function concircular, then constant.
منابع مشابه
The Scalar Curvature Equation on S 3
An obvious necessary condition for the existence of solutions to (1.1) is that the function K has to be positive somewhere. Moreover, there are the Kazdan-Warner obstructions [7, 16], which imply in particular, that a monotone function of the coordinate function X1 cannot be realized as the scalar curvature of a metric conformal to g0. Numerous studies have been made on equation (1.1) and its h...
متن کاملSolution of Vacuum Field Equation Based on Physics Metrics in Finsler Geometry and Kretschmann Scalar
The Lemaître-Tolman-Bondi (LTB) model represents an inhomogeneous spherically symmetric universefilledwithfreelyfallingdustlikematterwithoutpressure. First,wehaveconsideredaFinslerian anstaz of (LTB) and have found a Finslerian exact solution of vacuum field equation. We have obtained the R(t,r) and S(t,r) with considering establish a new solution of Rµν = 0. Moreover, we attempttouseFinslergeo...
متن کاملThe Scalar Curvature Deformation Equation on Locally Conformally Flat Manifolds
Abstract. We study the equation ∆gu− n−2 4(n−1)R(g)u+Ku p = 0 (1+ ζ ≤ p ≤ n+2 n−2 ) on locally conformally flat compact manifolds (M, g). We prove the following: (i) When the scalar curvature R(g) > 0 and the dimension n ≥ 4, under suitable conditions on K, all positive solutions u have uniform upper and lower bounds; (ii) When the scalar curvature R(g) ≡ 0 and n ≥ 5, under suitable conditions ...
متن کاملBlow-up in the Parabolic Scalar Curvature Equation
The parabolic scalar curvature equation is a reaction-diffusion type equation on an (n − 1)-manifold Σ, the time variable of which shall be denoted by r. Given a function R on [r0, r1)×Σ and a family of metrics γ(r) on Σ, when the coefficients of this equation are appropriately defined in terms of γ and R, positive solutions give metrics of prescribed scalar curvature R on [r0, r1)× Σ in the fo...
متن کاملPRESCRIBING SCALAR CURVATURE ON Sn
on S for n ≥ 3. In the case R is rotationally symmetric, the well-known Kazdan-Warner condition implies that a necessary condition for (1) to have a solution is: R > 0 somewhere and R′(r) changes signs. Then, (a) is this a sufficient condition? (b) If not, what are the necessary and sufficient conditions? These have been open problems for decades. In Chen & Li, 1995, we gave question (a) a nega...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: International electronic journal of geometry
سال: 2021
ISSN: ['1307-5624']
DOI: https://doi.org/10.36890/iejg.906792