A canonical connection is attached to any k-symplectic manifold. We study the properties of this connection and its geometric applications to k-symplectic manifolds. In particular, we prove that, under some natural assumptions, any k-symplectic manifold admits an Ehresmann connection, discuss some corollaries of this result and find vanishing theorems for characteristic classes on a k-symplectic manifold.
Some geometric structures associated with a k-symplectic manifold
CAPPELLETTI MONTANO, BENIAMINO;
2008-01-01
Abstract
A canonical connection is attached to any k-symplectic manifold. We study the properties of this connection and its geometric applications to k-symplectic manifolds. In particular, we prove that, under some natural assumptions, any k-symplectic manifold admits an Ehresmann connection, discuss some corollaries of this result and find vanishing theorems for characteristic classes on a k-symplectic manifold.
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