We study focal points and Maslov index of a horizontal geodesic gamma : I -> M in the total space of a semi-Riemannian submersion pi : M -> B by determining an explicit relation with the corresponding objects along the ...

We prove an estimate on the difference of Maslov indices relative to the choice of two distinct reference Lagrangians of a continuous path in the Lagrangian Grassmannian of a symplectic space. We discuss some applications ...

We consider a continuous path of bounded symmetric Fredholm bilinear forms with arbitrary endpoints on a real Hilbert space, and we prove a formula that gives the spectral flow of the path in terms of the spectral flow of ...

We discuss an algebraic theory for generalized Jordan chains and partial signatures, that are invariants associated to sequences of symmetric bilinear forms on a vector space. We introduce an intrinsic notion of partial ...

Given a one-parameter family {g(lambda) :lambda is an element of [ a, b]} of semi Riemannian metrics on an n-dimensional manifold M, a family of time-dependent potentials {V-lambda: lambda is an element of [a, b]} and a ...

We study the global centre symmetry set (GCS) of a smooth closed submanifold 'M POT.M'⊂'R POT.N', n≤2m . The GCS includes both the centre symmetry set defined by Janeczko (Geometria Dedicata 60:9–16, 1996) and the Wigner ...

Among the most important theories in physics is quantum mechanics which, in contrast to classical mechanics, uses topology in addition to differential geometry. Specifically, in this work, we will study the well-known ...