On the single-leaf Frobenius theorem and its applications
speaker: Paolo Piccione (Universidade de Sao Paulo, Brazil)abstract: Using the notion of Levi form of a smooth distribution, we discuss the local and the global problem of existence of one horizontal section of a smooth vector bundle endowed with a horizontal distribution. The analysis will lead to the formulation of a ``one-leaf'' analogue of the classical Frobenius integrability theorem in elementary differential geometry. Several applications of the result will be discussed. First, we will give a characterization of symmetric connections arising as Levi--Civita connections of semi-Riemannian metric tensors. Second, we will prove a general version of the classical Cartan--Ambrose--Hicks Theorem giving conditions on the existence of an affine map with prescribed differential at one point between manifolds endowed with connections.
timetable:
Sat 11 Mar, 10:00 - 11:00, Sala Conferenze Centro De Giorgi
<< Go back