This paper proposes a novel online domain-shift appearance learning and object tracking scheme on a Riemannian manifold for visual and infrared videos, especially for video scenarios containing large deformable objects with fast out-of-plane pose changes that could be accompanied by partial occlusions. Although Riemannian manifolds and covariance descriptors are promising for visual object trac...

We construct Parseval wavelet frames in $$L^2(M)$$ for a general Riemannian manifold M and we show the existence of unconditional $$L^p(M)$$ $$1< p <\infty $$ . This is made possible thanks to smooth orthogonal projection decomposition identity operator on , which was recently proven by Bownik et al. (Potential Anal 54:41–94, 2021). also characterization Triebel–Lizorkin $${\mathbf {F}}_{p,q}^s...

The results of this paper are related to a well-known problem, attributed to Hopf, to the effect that the Euler number χ(M2n) of a compact Riemannian manifold M2n of negative sectional curvature must satisfy the inequality (−1)nχ(M2n) > 0. This conjecture is true in dimensions 2 and 4 [Ch] and it has been verified in the Kähler case for all n by Gromov [G] and Stern [S] (the work in [S] also us...

Let M 2n be a compact Riemannian manifold of non-positive sectional curvature. It is shown that if M 2n is homeomorphic to a KK ahler manifold, then its Euler number satisses the inequality (?1) n (M 2n) 0. Introduction The results of this paper are related to a well-known problem, attributed sometimes to Hopf and sometimes to Chern, to the eeect that the Euler number (M 2n) of a compact Rieman...

Let X and B be two Riemannian manifolds with π : X → B being a Riemannian submersion. Let H be the corresponding horizontal distribution, which is perpendicular to the tangent bundle of the fibres of π : X → B. Then X (just considered as a differentiable manifold), together with the distribution H, forms a so-called Carnot-Caratheodory space [1], when the Riemannian metric of X is restricted to...

In this article, we propose a control law for almostglobal asymptotic tracking (AGAT) of a smooth reference trajectory for a fully actuated simple mechanical system (SMS) evolving on a Riemannian manifold which can be embedded in a Euclidean space. The existing results on tracking for an SMS are either local, or almost-global, only in the case the manifold is a Lie group. In the latter case, th...

‎The object of the present paper is to introduce and study a type of non-flat semi-Riemannian manifolds‎, ‎called‎, ‎super generalized recurrent manifolds which generalizes both the notion of hyper generalized recurrent manifolds [‎A.A‎. ‎Shaikh and A‎. ‎Patra‎, On a generalized class of recurrent manifolds‎, Arch‎. ‎Math‎. ‎(Brno) 46 (2010) 71--78‎.] and weakly generalized recurrent manifolds ...