operator-valued tensors on manifolds
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abstract
in this paper we try to extend geometric concepts in the context of operator valued tensors. to this end, we aim to replace the field of scalars $ mathbb{r} $ by self-adjoint elements of a commutative $ c^star $-algebra, and reach an appropriate generalization of geometrical concepts on manifolds. first, we put forward the concept of operator-valued tensors and extend semi-riemannian metrics to operator valued metrics. then, in this new geometry, some essential concepts of riemannian geometry such as curvature tensor, levi-civita connection, hodge star operator, exterior derivative, divergence,... will be considered.
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Journal title:
bulletin of the iranian mathematical societyجلد ۴۲، شماره ۵، صفحات ۱۲۵۹-۱۲۷۷
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