지원사업
학술연구/단체지원/교육 등 연구자 활동을 지속하도록 DBpia가 지원하고 있어요.
커뮤니티
연구자들이 자신의 연구와 전문성을 널리 알리고, 새로운 협력의 기회를 만들 수 있는 네트워킹 공간이에요.
초록· 키워드
오류제보하기
On a compact $n$-dimensional manifold $M$, it has been conjectured that a critical point of the total scalar curvature, restricted to the space of metrics with constant scalar curvature of unit volume, is Einstein. In this paper, after derivng an interesting curvature identity, we show that the conjecture is true in dimension three and four when $g$ is weakly Einstein. In higher dimensional case $n\geq 5$, we also show that the conjecture is true under an additional Ricci curvature bound. Moreover, we prove that the manifold is isometric to a standard $n$-sphere when it is $n$-dimensional weakly Einstein and the kernel of the linearized scalar curvature operator is nontrivial.
목차
등록된 정보가 없습니다.
참고문헌 (9)
참고문헌 신청
M. Berger / 1970 / Quelques formules de variation pour une structure riemannienne / Ann. Sci. E cole Norm. Sup. (4) 3:285~294
A. L. Besse / 1987 / Einstein Manifolds / Ergeb. Math. Grenzgeb. (3) 10
Y. Euh / 2013 / A curvature identity on a 4-dimensional Riemann-ian manifold / Results Math 63(1-2):107~114
N. Koiso / 1979 / A decomposition of the space M of Riemannian metrics on a manifold / Osaka J. Math 16(2):423~429
J. Lafontaine / 1982 / Remarques sur les vari´et´es conformement plates / Math. Ann 259(3):313~319
A. L. Besse / 1987 / Einstein Manifolds / Ergeb. Math. Grenzgeb. (3) 10
Y. Euh / 2013 / A curvature identity on a 4-dimensional Riemann-ian manifold / Results Math 63(1-2):107~114
N. Koiso / 1979 / A decomposition of the space M of Riemannian metrics on a manifold / Osaka J. Math 16(2):423~429
J. Lafontaine / 1982 / Remarques sur les vari´et´es conformement plates / Math. Ann 259(3):313~319
함께 읽어보면 좋을 논문
논문 유사도에 따라 DBpia 가 추천하는 논문입니다. 함께 보면 좋을 연관 논문을 확인해보세요!
-
Stability of total scalar curvature and the critical point equation
대한수학회보
2024 .01
-
Some rigidity characterizations of Einstein metrics as critical points for quadratic curvature functionals
대한수학회보
2020 .01
-
On the geometry of vector bundles with flat connections
대한수학회보
2019 .01
-
On conformally flat polynomial $(\alpha,\beta)$-metrics with weakly isotropic scalar curvature
대한수학회지
2019 .01
-
On homogeneous square Einstein metrics
대한수학회보
2017 .01
-
Deformation of Cartan curvature on Finsler manifolds
대한수학회보
2017 .01
-
Generalized Quasi-Einstein Metrics and Contact Geometry
Kyungpook Mathematical Journal
2022 .09
-
η-Einstein Solitons on (ε)-Kenmotsu Manifolds
Kyungpook Mathematical Journal
2020 .01
-
On weakly Einstein almost contact manifolds
대한수학회지
2020 .01
-
Gradient Einstein-type contact metric manifolds
대한수학회논문집
2020 .01
-
CURVATURES ON THE ABBENA-THURSTON MANIFOLD
호남수학학술지
2016 .01
-
Z Tensor on N(k)-Quasi-Einstein Manifolds
Kyungpook Mathematical Journal
2016 .01
-
Einstein's connection in $3$-dimensional $ES$-manifold
한국수학논문집
2015 .01
-
Some results in $\eta$-Ricci soliton and gradient $\rho$-Einstein soliton in a complete Riemannian manifold
대한수학회논문집
2019 .01
-
Some properties of critical point equations metrics on the statistical manifolds
대한수학회논문집
2024 .04
-
Gradient Yamabe solitons with conformal vector field
대한수학회논문집
2021 .01
-
AN ALGEBRAIC SOLUTION OF EINSTEIN'S FIELD EQUATIONS IN X<sub>4</sub>
충청수학회지
2015 .01
-
Super Quasi-Einstein Manifolds with Applications to General Relativity
Kyungpook Mathematical Journal
2018 .01
-
Scalar curvature comparisons of level hypersurfaces of geodesic spheres
대한수학회보
2018 .01
-
On the closed Einstein-Weyl structure and compact $K$-contact manifold
대한수학회보
2016 .01
이 논문의 저자 정보
최근 본 자료
댓글(0)
0