Null submanifolds and statistical connections in indefinite Kähler manifolds

Abstract

A holomorphic statistical connection in an indefinite Kähler manifold induces in a natural way a statistical connection in a nondegenerate submanifold, but not if the submanifold is degenerate. In the case of a null hypersurface in an indefinite Kähler manifold, we construct a new nondegenerate metric on the null hypersurface and we study conditions for the induced connection to be statistical with respect to it. This construction involves the almost complex structure, thereby extending to the Kähler case a previous work. We also study the case of codimension two invariant null submanifolds, showing that the above construction only provides trivial statistical connections.

Keywords

• null submanifolds
• statistical manifold
• dual connection
• holomorphic connection
• Kähler manifold

References

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