Solvability for perturbations of a class of real vector fields on the two-torus

2020 ◽  
Vol 492 (2) ◽  
pp. 124467
Author(s):  
Paulo L. Dattori da Silva ◽  
Rafael B. Gonzalez ◽  
Marcio A. Jorge Silva
Keyword(s):  
Vector Fields ◽  
Real Vector

scholarly journals Global Hölder Estimates via Morrey Norms for Hypoelliptic Operators with Drift

2017 ◽  
Vol 2017 ◽  
pp. 1-6
Author(s):  
Yuexia Hou ◽  
Pengcheng Niu
Keyword(s):  
Vector Fields ◽  
Integral Operators ◽  
Morrey Spaces ◽  
Homogeneous Group ◽  
Hypoelliptic Operator ◽  
Real Vector ◽  
Constant Matrix ◽  
Hypoelliptic Operators ◽  
Hölder Estimates

Suppose thatX0,X1,…,Xmare left invariant real vector fields on the homogeneous groupGwithX0being homogeneous of degree two andX1,…,Xmhomogeneous of degree one. In the paper we study the hypoelliptic operator with drift of the kindL=∑i,j=1maijXiXj+a0X0,wherea0≠0and(aij)is a constant matrix satisfying the elliptic condition onRm. By proving the boundedness of two integral operators on the Morrey spaces with two weights, we obtain global Hölder estimates forL.

A GENERALIZATION OF THE ATIYAH–DUPONT VECTOR FIELDS THEORY

2002 ◽  
Vol 04 (04) ◽  
pp. 777-796 ◽  
Author(s):  
ZIZHOU TANG ◽  
WEIPING ZHANG
Keyword(s):  
Vector Bundle ◽  
Cross Sections ◽  
Vector Fields ◽  
Complex Structure ◽  
Index Theory ◽  
Index Theorem ◽  
Obstruction Theory ◽  
Real Vector ◽  
Complete Answer ◽  
Linearly Independent

To generalize the Hopf index theorem and the Atiyah–Dupont vector fields theory, one is interested in the following problem: for a real vector bundle E over a closed manifold M with rank E = dim M, whether there exist two linearly independent cross sections of E? We provide, among others, a complete answer to this problem when both E and M are orientable. It extends the corresponding results for E = TM of Thomas, Atiyah, and Atiyah–Dupont. Moreover we prove a vanishing result of a certain mod 2 index when the bundle E admits a complex structure. This vanishing result implies many known famous results as consequences. Ideas and methods from obstruction theory, K-theory and index theory are used in getting our results.

scholarly journals Flags in zero dimensional complete intersection algebras and indices of real vector fields

2007 ◽  
Vol 260 (1) ◽  
pp. 77-91 ◽  
Author(s):  
L. Giraldo ◽  
X. Gómez-Mont ◽  
P. Mardešić
Keyword(s):  
Complete Intersection ◽  
Vector Fields ◽  
Real Vector
Sign in / Sign up

Export Citation Format

Share Document