On Killing tensors in Riemannian manifolds of positive curvature operator
نویسندگان
چکیده
منابع مشابه
Killing-Poisson tensors on Riemannian manifolds
We introduce a new class of Poisson structures on a Riemannian manifold. A Poisson structure in this class will be called a Killing-Poisson structure. The class of Killing-Poisson structures contains the class of symplectic structures, the class of Poisson structures studied in (Differential Geometry and its Applications, Vol. 20, Issue 3 (2004), 279–291) and the class of Poisson structures ind...
متن کاملOperator-valued tensors on manifolds
In this paper we try to extend geometric concepts in the context of operator valued tensors. To this end, we aim to replace the field of scalars $ mathbb{R} $ by self-adjoint elements of a commutative $ C^star $-algebra, and reach an appropriate generalization of geometrical concepts on manifolds. First, we put forward the concept of operator-valued tensors and extend semi-Riemannian...
متن کاملSturm-Liouville operator controlled by sectional curvature on Riemannian manifolds
The purpose of this paper is fourfold: (1) to introduce and study a second order PDE, determined accidentally by a Riemann wave, reflecting the connection between oriented parallelograms area and sectional curvature on Riemannian manifolds; (2) to introduce and study the asymptotic behavior of oriented parallelograms area controlled by the sectional curvature; (3) to study some partial differen...
متن کاملCompact 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 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: Tohoku Mathematical Journal
سال: 1976
ISSN: 0040-8735
DOI: 10.2748/tmj/1178240832