Riemannian Manifolds with Positive Yamabe Invariant and Paneitz Operator
نویسندگان
چکیده
منابع مشابه
Compact Riemannian Manifolds with Positive Curvature Operators
M is said to have positive curvature operators if the eigenvalues of Z are positive at each point p € M. Meyer used the theory of harmonic forms to prove that a compact oriented n-dimensional Riemannian manifold with positive curvature operators must have the real homology of an n-dimensional sphere [GM, Proposition 2.9]. Using the theory of minimal two-spheres, we will outline a proof of the f...
متن کاملRiemannian Manifolds with Positive Sectional Curvature
It is fair to say that Riemannian geometry started with Gauss’s famous ”Disquisitiones generales” from 1827 in which one finds a rigorous discussion of what we now call the Gauss curvature of a surface. Much has been written about the importance and influence of this paper, see in particular the article [Do] by P.Dombrowski for a careful discussion of its contents and influence during that time...
متن کاملThe Laplace-Beltrami-Operator on Riemannian Manifolds
This report mainly illustrates a way to compute the Laplace-Beltrami-Operator on a Riemannian Manifold and gives information to why and where it is used in the Analysis of 3D Shapes. After a brief introduction, an overview over the necessary properties of manifolds for calculating the Laplacian is given. Furthermore the two operators needed for defining the Laplace-Beltrami-Operator the gradien...
متن کاملThe Yamabe invariant for non-simply connected manifolds
The Yamabe invariant is an invariant of a closed smooth manifold defined using conformal geometry and the scalar curvature. Recently, Petean showed that the Yamabe invariant is non-negative for all closed simply connected manifolds of dimension ≥ 5. We extend this to show that Yamabe invariant is non-negative for all closed manifolds of dimension ≥ 5 with fundamental group of odd order having a...
متن کاملOn invariant operations on pseudo-Riemannian manifolds
Invariant polynomial operators on Riemannian manifolds are well understood and the knowledge of full lists of them becomes an effective tool in Riemannian geometry, [Atiyah, Bott, Patodi, 73] is a very good example. The present short paper is in fact a continuation of [Slovák, 92] where the classification problem is reconsidered under very mild assumptions and still complete classification resu...
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 Mathematics Research Notices
سال: 2015
ISSN: 1073-7928,1687-0247
DOI: 10.1093/imrn/rnv176