We study the weighted ray transform of integrating functions on a Lorentzian manifold over lightlike geodesics. We prove support theorems if the manifold and the weight are analytic.

M.A. Akyol and B. Şahin [Conformal anti-invariant Riemannian maps to Kaehler manifolds, U.P.B. Sci. Bull., Series A, Vol. 80, Iss. 4, 2018] defined studied the notion of conformal manifolds. In this paper, as a generalization totally real submanifolds maps, we extend almost contact metric manner, introduce from manifolds cosymplectic order guarantee existence notion, give non-trivial example, i...

We study the semi-Riemannian geometry of foliation F an indefinite locally conformal Kähler (l.c.K.) manifold M, given by Pfaffian equation ω=0, provided that ∇ω=0 and c=∥ω∥≠0 (ω is Lee form M). If M conformally flat then every leaf shown to be a totally geodesic hypersurface in space sectional curvature c/4, carrying c-Sasakian structure. As corollary result together with version de Rham decom...

Spinors are lightlike. How do they combine to make massive particles? We visit the zoo of Lagrangian singularities, or caustics, in spacetime projections from spin spacethe phase space of lightlike, 8spinor flows. We find that the species living there are the elementary particles. Codimension J = (1, 2, 3, 4) phase singularities vortex lines, sheets, tubes, and knots, are classified by the Coxe...

In this paper, we discuss submersion of CR-submanifolds of locally conformal Kaehler manifold. We prove that if π : M −→ B◦ is a submersion of CR-submanifold M of a locally conformal Kaehler manifoldM onto an almost Hermitian manifold B◦, then B◦ is a locally conformal Kaehler manifold. Furthermore, we discuss totally umbilical CR-submanifold and cohomology of CR-submanifold of locally conforma...

In contrast with the three-dimensional case (cf. Montezuma in Bull Braz Math Soc), where rotationally symmetric totally geodesic free boundary minimal surfaces have Morse index one; we prove this work that of a hypersurface n-dimensional Riemannnian Schwarzschild space respect to variations are tangential along horizon is zero, for \(n\ge 4\). Moreover, show there exist non-compact hypersurface...

We introduce a new geometrical invariant of CR manifolds hypersurface type, which we call the “Levi core” manifold. When manifold is boundary smooth bounded pseudoconvex domain, show how Levi core related to two other important global invariants in several complex variables: Diederich–Fornæss index and D’Angelo class (namely set forms boundary). also that trivial whenever domain finite-type sen...

The outward–pointing principal null direction of the Schwarzschild Rie-mann tensor is null hypersurface–forming. If the Schwarzschild mass spontaneously jumps across one such hypersurface then the hypersurface is the history 1 of an outgoing light–like shell. The outward– pointing principal null direction of the Kerr Riemann tensor is asymptotically (in the neighbourhood of future null infinity...

Background: Antenatal steroid therapy recently has been considered for term and late preterm neonates delivered by Cesarean section (CS), with the aim of preventing adverse respiratory morbidity. The main aim of this study was to investigate the metabolic effects of antenatal dexamethasone on blood glucose (BG), homeostasis, and serum C-peptide level when administered to term fetuses. Methods: ...