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Our motivation for studying this problem is threefold:
(i) When one fixes r = m = 0, the resulting two parameter family is a normal
form for a codimension two bifurcation within the class of planar ...
This is an announcement of our work [5] on introducing and studying a geometric heat flow to find Killing vector fields on closed Riemannian manifolds with positive sectional curvature. We study its v...
Transitive Lie algebras of vector fields---an overview
Transitive Lie algebras vector fields Differential Geometry
2011/9/6
Abstract: This overview paper is intended as a quick introduction to Lie algebras of vector fields. Originally introduced in the late 19th century by Sophus Lie to capture symmetries of ordinary diffe...
A geometric heat flow for vector fields
Geometric heat flow Killing vector fields Yano’s theorem Navier-Stokes equations
2011/9/6
Abstract: This is an announcement of our work [5] on introducing and studying a geometric heat flow to find Killing vector fields on closed Riemannian manifolds with positive sectional curvature. We s...
On vector fields having properties of Reeb fields
Reeb field presymplectic form contact form geodesible field
2011/9/5
Abstract: We study constructions of vector fields with properties which are characteristic to Reeb vector fields of contact forms. In particular, we prove that all closed oriented odd-dimensional mani...
Estimates on the modulus of expansion for vector fields solving nonlinear equations
Estimates vector fields nonlinear equations Differential Geometry
2011/9/5
Abstract: By adapting methods of \cite{AC} we prove a sharp estimate on the expansion modulus of the gradient of the log of the parabolic kernel to the Sch\"ordinger operator with convex potential, wh...
Conformal Killing vector fields and Rellich type identities on Riemannian Manifolds, II
Riemannian Manifolds Killing vector fields Rellich identities
2011/1/21
We propose a general Noetherian approach to Rellich integral identities. Using this method we obtain a higher order Rellich type identity involving the polyharmonic operator on Riemannian manifolds ad...
The span of a manifold is its maximum number of linearly independent vector fields. We discuss the question, still unresolved, of whether span(Pm × Pn) always equals span(Pm)+span(Pn). Here Pn denotes...