Ela the Linear Independence of Sets of Two and Three Canonical Algebraic Curvature Tensors
نویسندگان
چکیده
We generalize the construction of canonical algebraic curvature tensors by selfadjoint endomorphisms of a vector space to arbitrary endomorphisms. Provided certain basic rank requirements are met, we establish a converse of the classical fact that if A is symmetric, then RA is an algebraic curvature tensor. This allows us to establish a simultaneous diagonalization result in the event that three algebraic curvature tensors are linearly dependent. We use these results to establish necessary and sufficient conditions that a set of two or three algebraic curvature tensors be linearly independent. We present the proofs of these results using elementary methods.
منابع مشابه
The Linear Independence of Sets of Two and Three Canonical Algebraic Curvature Tensors
Provided certain basic rank requirements are met, we establish a converse of the classical fact that if A is symmetric, then RA is an algebraic curvature tensor. This allows us to establish a simultaneous diagonalization result in the event that three algebraic curvature tensors are linearly dependent. We use these results to establish necessary and sufficient conditions that a set of two or th...
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