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Recenti sviluppi della geometria complessa, differenziale, simplettica

Iterated Differential Forms and Tensors

speaker: Luca Vitagliano (Università degli studi di Salerno)

abstract: We present general theory and some applications of "Iterated Differential Forms" (IDFs), i.e., differential forms over a differential form algebra. Covariant tensors over a manifold M are naturally interpreted as IDFs over M. As an application of this result we formulate Riemannian Geometry in terms of IDFs. Levi-Civita connection, Riemann tensor, Ricci tensor can be obtained from the "metric form" by applying suitable natural operators of the integro-differential calculus over the algebra of IDFs. The new interpretation of the metric tensor as an IDF allows useful generalizations (Riemannian graded-geometry, secondary Riemannian geometry, etc.).

timetable:
Sat 11 Mar, 12:40 - 13:00, Sala Conferenze Centro De Giorgi
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