Complex Structures on Real Vector Bundles

1967 ◽  
Vol 89 (4) ◽  
pp. 887 ◽  
Author(s):  
Emery Thomas
Keyword(s):  
Vector Bundles ◽  
Complex Structures ◽  
Real Vector

STRING EQUATIONS OF MOTION FROM VANISHING CURVATURE

1991 ◽  
Vol 06 (08) ◽  
pp. 1319-1333 ◽  
Author(s):  
MARK J. BOWICK ◽  
KONG-QING YANG
Keyword(s):  
Vector Bundles ◽  
Adiabatic Approximation ◽  
Equations Of Motion ◽  
Bosonic String ◽  
Complex Structures ◽  
Closed Bosonic String

The equations of motion for the massless modes of the closed bosonic string are obtained in the adiabatic approximation from the requirement of the vanishing of the curvature of appropriate vector bundles over the space of complex structures Diff S1/S1. This vanishing is required for physical states to be independent of string parametrization.

On complex structures in 8-dimensional vector bundles

1998 ◽  
Vol 95 (1) ◽  
pp. 323-330 ◽  
Author(s):  
Martin Čadek ◽  
Jiří Vanžura
Keyword(s):  
Vector Bundles ◽  
Complex Structures ◽  
Dimensional Vector

Sums of stably trivial vector bundles

1980 ◽  
Vol 87 (1) ◽  
pp. 97-107 ◽  
Author(s):  
Jacques Allard
Keyword(s):  
Vector Bundle ◽  
Line Bundle ◽  
Vector Bundles ◽  
Real Vector

We say that a real vector bundle ξ over a finite C.W. complex X is stably trivial of type (n, k) or, simply, of type (n, k) if ξ ⊕ kε ≅ nε, where ε denotes a trivial line bundle. The following theorem is an immediate corollary (see (12)) of a theorem of T. Y. Lam ((9), theorem 2).

Linear symplectic geometry

2017 ◽  
Author(s):  
Dusa McDuff ◽  
Dietmar Salamon
Keyword(s):  
Symplectic Geometry ◽  
Vector Bundles ◽  
Maslov Index ◽  
Vector Spaces ◽  
Complex Structures ◽  
Homotopy Equivalence ◽  
Linear Complex ◽  
Symplectic Forms ◽  
Lagrangian Subspaces ◽  
First Chern Class

The second chapter introduces the basic concepts of symplectic topology in the linear algebra setting, such as symplectic vector spaces, the linear symplectic group, Lagrangian subspaces, and the Maslov index. In the section on linear complex structures particular emphasis is placed on the homotopy equivalence between the space of symplectic forms and the space of linear complex structures. The chapter includes sections on symplectic vector bundles and the first Chern class.

Sign in / Sign up

Export Citation Format

Share Document