We consider subordination chains of simply connected domains with smooth boundaries in the complex plane. Such chains admit Hamiltonian and Lagrangian interpretations through the Löwner-Kufarev evolution equations. The action functional is constructed and its time variation is obtained. It represents the infinitesimal version of the action of the Virasoro-Bott group over the space of analytic u...

We study the quaternion CR-submanifolds of a quaternion Kaehler manifold. More specifically we study the properties of the canonical structures and the geometry of the canonical foliations by using the Bott connection and the index of a quaternion CR-submanifold. 2000 Mathematics Subject Classification. 53C20, 53C21, 53C25.

The occurrence of conical refraction in hexagonal and in cubic elastic media is investigated by the method of localizations. This is accomplished by generalizing the Atiyah–Bott– G̊arding theory from the scalar case to hyperbolic square systems of linear partial differential systems with constant coefficients.

We construct an explicit basis for the coordinate ring of the Bott-Samelson variety Zi associated to G = GL(n) and an arbitrary sequence of simple reflections i. Our basis is parametrized by certain standard tableaux and generalizes the Standard Monomial basis for Schubert varieties. In this paper, we prove the results announced in [LkMg] for the case of Type An−1 (the groups GL(n) and SL(n)). ...