We prove the vanishing of the Dolbeault cohomology groups on Hermitian manifolds with ddc-harmonic Kähler form and positive (1, 1)-part of the Ricci form of the Bismut connection. This implies the vanishing of the Dolbeault cohomology groups on complex surfaces which admit a conformal class of Hermitian metrics, such that the Ricci tensor of the canonical Weyl structure is positive. As a coroll...

This study explored the claim that invariant acoustic properties corresponding to phonetic features generalize across languages. Experiment I examined whether the same invariant properties can characterize diffuse stop consonants in Malayalam, French, and English. Results showed that, contrary to theoretical predictions, we could not distinguish labials from dentals, nor could we classify denta...

We present two methods for generating trajectories and motion interpolants that minimize energy functionals on SE(3), the group of rigid body displacements. We treat SE(3) as a Lie Group and endow it with a left-invariant Riemannian metric derived from energy considerations. The first method is based on a relaxation formulation where the Euler-Lagrange equations for the minimization problem are...

We classify solvable Lie groups with a free nilradical admitting an Einstein left-invariant metric. Any such group is essentially determined by the nilradical of its Lie algebra, which is then called an Einstein nilradical. We show that among the free Lie algebras, there are very few Einstein nilradicals. Except for the one-step (abelian) and the two-step ones, there are only six (here f(m, p) ...

We use the geometry of the geodesics of a certain left-invariant metric on the Lie group Sp(2) to find explicit related formulas for two topological objects: the Blakers-Massey element (a generator of π6(S)) and an exotic (i.e. not isotopic to the identity) diffeomorphism of S6 (C. E. Durán, 2001). These formulas depend on two quaternions and their conjugates and we produce their extensions to ...

We classify solvable Lie groups with a free nilradical admitting an Einstein left-invariant metric. Any such group is essentially determined by the nilradical of its Lie algebra, which is then called an Einstein nilradical. We show that among the free Lie algebras, there are very few Einstein nilradicals. Except for the one-step (abelian) and the two-step ones, there are only six (here f(m, p) ...

In the present article we show how to produce new examples of integrable dynamical systems of differential geometry origin. This is based on a construction of a canonical Hamiltonian structure for the geodesic flows of Carnot–Carathéodory metrics ([7, 17]) via the Pontryagin maximum principle. This Hamiltonian structure is achieved by introducing Lagrange multipliers bundles being the phase spa...

This paper shows that the left-invariant geodesic flow on the symplectic group relative to the Frobenius metric is an integrable system that is not contained in the Mishchenko-Fomenko class of rigid body metrics. This system may be expressed as a flow on symmetric matrices and is bi-Hamiltonian. This analysis is extended to cover flows on symmetric matrices when an isomorphism Research partiall...