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This paper focuses on the study of three dimensional real hypersurfaces in non-flat complex space forms whose $^{*}$-Ricci tensor satisfies conditions of parallelism. More precisely, extension of existing results concerning real…
In this study, we give definition of some multivalued hybrid mappings which are general than many mappings in the existing literature, then we give some existence and convergence results for these mappings in CAT({\kappa})-spaces
In this paper, we obtain Chen's inequalities for submanifolds in $(\kappa,\mu)$-contact space form with two kinds of generalized semi-symmetric non-metric connections.
We introduce a class of null hypersurfaces of a semi-Riemannian manifold, namely, screen quasi-conformal hypersurfaces, whose geometry may be studied through the geometry of its screen distribution. In particular, this notion allows us to…
We study the geometry of null hypersurfaces in indefinite complex contact manifolds. We prove several classification results for a variety of well-known null hypersurfaces, including the totally umbilic, totally screen umbilic, and the…
In this paper we extend the theory of H-closed extensions of Hausdorff spaces to a class of non-Hausdorff spaces, defined in \cite{B}, called $n$-Hausdorff spaces. The notion of H-closed is generalized to an $n$-H-closed space. Known…
Hypersurfaces are studied and classified under multiple additional assumptions in any Riemannian homogeneous space $(\mathbb{C}P^3, g_a)$, including nearly K\"ahler $\mathbb{C}P^3$. Notably, all extrinsically homogeneous hypersurfaces are…
The distribution of the deformations of elementary cells is studied in an abstract lattice constructed from the existence of the empty set. One combination rule determining oriented sequences with continuity of set-distance function in such…
Based on a well-known fact that there are no Einstein hypersurfaces in a non-flat complex space form, in this article we study the quasi-Einstein condition, which is a generalization of an Einstein metric, on the real hyersurface of a…
The multiplicity distributions produced by the variation of time-dependent gravitational fields in a conformally flat background geometry belong to the same class of infinitely divisible distributions found, for fixed centre of mass…
A Tychonoff space $X$ is called $\kappa$-pseudocompact if for every continuous mapping $f$ of $X$ into $\mathbb{R}^\kappa$ the image $f(X)$ is compact. This notion generalizes pseudocompactness and gives a stratification of spaces lying…
By Hartman--Nirenberg's theorem, any complete flat hypersurface in Euclidean space must be a cylinder over a plane curve. However, if we admit some singularities, there are many non-trivial examples. Flat fronts are flat hypersurfaces with…
We extend the framework of general boundary quantum field theory (GBQFT) to achieve a fully local description of realistic quantum field theories. This requires the quantization of non-K\"ahler polarizations which occur generically on…
The properties of multimomentum maps on null hypersurfaces, and their relation with the constraint analysis of General Relativity, are described. Unlike the case of spacelike hypersurfaces, some constraints which are second class in the…
In this article we study Brill-Noether loci of moduli space of stable bundles over smooth surfaces. We define Petri map as an analogy with the case of curves. We show the non-emptiness of certain Brill-Noether loci over very general quintic…
This thesis is framed within the field of Mathematical Relativity and is organized into six chapters. After an introduction to the topic in Chapter 1, Chapter 2 reviews and further develops the formalism of hypersurface data, which provides…
The recently investigated Hilbert-Krein and other positivity structures of the superspace are considered in the framework of superdistributions. These tools are applied to problems raised by the rigorous supersymmetric quantum field theory.
We employ the formalism of vanishing cycles and perverse sheaves to introduce and study the vanishing cohomology of complex projective hypersurfaces. As a consequence, we give upper bounds for the Betti numbers of projective hypersurfaces,…
The aim of this paper is to complete the local classification of minimal hypersurfaces with vanishing Gauss-Kronecker curvature in a 4-dimensional space form. Moreover, we give a classification of complete minimal hypersurfaces with…
$2$-nondegenerate real hypersurfaces in complex manifolds play an important role in CR-geometry and the theory of Hermitian Symmetric Domains. In this paper, we construct a complete convergent normal form for everywhere $2$-nondegenerate…