Question de licence. Faculté des sciences de Paris, 7 juillet 1868
On normal CR-submanifolds of S-manifolds
Many authors have studied the geometry of submanifolds of Kaehlerian and Sasakian manifolds. On the other hand, David E. Blair has initiated the study of S-manifolds, which reduce, in particular cases, to Sasakian manifolds ([1, 2]). I. Mihai ([8]) and L. Ornea ([9]) have investigated CR-submanifolds of S-manifolds. The purpose of the present paper is to study a special kind of such submanifolds, namely the normal CR-submanifolds. In Sections 1 and 2, we review basic formulas and definitions for...
On the moduli space of superminimal surfaces in spheres.
CR-products of S-manifolds
«El desorden absoluto es imposible»: la Teoría de Ramsey.
Controllability properties for the one-dimensional Heat equation under multiplicative or nonnegative additive controls with local mobile support
We discuss several new results on nonnegative approximate controllability for the one-dimensional Heat equation governed by either multiplicative or nonnegative additive control, acting within a proper subset of the space domain at every moment of time. Our methods allow us to link these two types of controls to some extend. The main results include approximate controllability properties both for the static and mobile control supports.
Identification of a quasilinear parabolic equation from final data
We study the identification of the nonlinearities A,(→)b and c appearing in the quasilinear parabolic equation y_t − div(A(y)∇y + (→)b(y)) + c(y) = u inΩ × (0,T), assuming that the solution of an associated boundary value problem is known at the terminal time, y(x,T), over a (probably small) subset of Ω, for each source term u. Our work can be divided into two parts. Firstly, the uniqueness of A,(→)b and c is proved under appropriate assumptions. Secondly, we consider a finite-dimensional optimization...
Optimal control of quasilinear elliptic equations with non differentiable coefficients at the origin.
In this paper we study some optimal control problems of systems governed by quasilinear elliptic equations in divergence form with non differentiable coefficients at the origin. We prove existence of solutions and derive the optimality conditions by considering a perturbation of the differential operator coefficients that removes the singularity at the origin. Regularity of optimal controls is also deduced.
A classification of certain submanifolds of an S-manifold
A classification theorem is obtained for submanifolds with parallel second fundamental form of an 𝑆-manifold whose invariant f-sectional curvature is constant.
Minimal slant submanifolds of the smallest dimension in S-manifolds.
We study slant submanifolds of S-manifolds with the smallest dimension, specially minimal submanifolds and establish some relations between them and anti-invariant submanifolds in S-manifolds, similar to those ones proved by B.-Y. Chen for slant surfaces and totally real surfaces in Kaehler manifolds.
Curvature properties of a semi-symmetric metric connection on S-manifolds
In this study, S-manifolds endowed with a semi-symmetric metric connection naturally related with the S-structure are considered and some curvature properties of such a connection are given. In particular, the conditions of semi-symmetry, Ricci semi-symmetry and Ricci-projective semi-symmetry of this semi-symmetric metric connection are investigated.
Generalized -space-forms
On certain anti-invariant submanifolds of an S-manifold
Discrete Morse inequalities on infinite graphs.
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