Two special Finsler spaces have been introduced and investigated, namely R-recurrent Finsler space and concircularly recurrent Finsler space. The defining properties of these spaces are formulated in terms of the first curvature tensor of Cartan connection. The following three results constitute the main object of the present paper: (i) a concircularly flat Finsler manifold is necessarily of co...

We generalize the hyper-systolic algorithm proposed in [1] for abstract data structures on massive parallel computers with np processors. For a problem of size V the communication complexity of the hyper-systolic algorithm is proportional to √ npV , to be compared with npV for the systolic case. The implementation technique is explained in detail and the example of the parallel matrix-matrix mu...

Hyper-sensitivity to unknown boundary conditions plagues indirect methods of solving optimal control problems as a Hamiltonian boundary-value problem for both state and costate. Yet the hyper-sensitivity may imply manifold structure in the Hamiltonian flow, knowledge of which would yield insight regarding the optimal solutions and suggest a solution approximation strategy that circumvents the h...

Abstract We consider piecewise-smooth dynamical systems, i.e., systems of ordinary differential equations switching between different sets on distinct domains, separated by hyper-surfaces. As is well-known, when the solution approaches a discontinuity manifold, classical may cease to exist. For this reason, starting with pioneering work Filippov, concept weak (also known as sliding mode) has be...

The Lax formulation of the hyper-Hermiticity condition in four dimensions is used to derive a potential that generalises Plebanski’s second heavenly equation for hyper-Kahler 4-manifolds. A class of examples of hyper-Hermitian metrics which depend on two arbitrary functions of two complex variables is given. The twistor theory of four-dimensional hyper-Hermitian manifolds is formulated as a com...

We find that the target space of two-dimensional (4,0) supersymmetric sigma models with torsion coupled to (4,0) supergravity is a QKT manifold, that is, a quaternionic Kahler manifold with torsion. We give four examples of geodesically complete QKT manifolds one of which is a generalisation of the LeBrun geometry. We then construct the twistor space associated with a QKT manifold and show that...

We show any Riemannian curvature model can be geometrically realized by a manifold with constant scalar curvature. We also show that any pseudo-Hermitian curvature model, para-Hermitian curvature model, hyperpseudo-Hermitian curvature model, or hyper-para-Hermitian curvature model can be realized by a manifold with constant scalar and ⋆-scalar curvature.

Recent authors have investigated the use of manifolds and Lie group methods for independent component analysis (ICA), including the Stiefel and the Grassmann manifolds and the orthogonal group O(n). In this paper we introduce a new class of manifold, the generalized flag manifold, which is suitable for independent subspace analysis. The generalized flag manifold is a set of subspaces which are ...