Related papers: Special Geometry, Hessian Structures and Applicati…
We study the dimensional reduction of five dimensional N=2 Yang-Mills-Einstein supergravity theories (YMESGT) coupled to tensor multiplets. The resulting 4D theories involve first order interactions among tensor and vector fields with mass…
Freudenthal duality, introduced in L. Borsten, D. Dahanayake, M. J. Duff and W. Rubens, Phys.Rev. D80, 026003 (2009), and defined as an anti-involution on the dyonic charge vector in d = 4 space-time dimensions for those dualities admitting…
The Hessian geometry is the real analogue of the K\"ahler one. Sasakian geometry is an odd-dimensional counterpart of the K\"ahler geometry. In the paper, we study the connection between projective Hessian and Sasakian manifolds analogous…
One-dimensional sigma-models with N supersymmetries are considered. For conventional supersymmetries there must be N-1 complex structures satisfying a Clifford algebra and the constraints on the target space geometry can be formulated in…
We study imbedded hypersurfaces in spacetime whose causal character is allowed to change from point to point. Inherited geometrical structures on these hypersurfaces are defined by two methods: first, the standard rigged connection induced…
We consider the classification of near-horizon geometries in a general two-derivative theory of gravity coupled to abelian gauge fields and uncharged scalars in four and five dimensions, with one and two commuting rotational symmetries…
The existing classification of homogeneous quaternionic spaces is not complete. We study these spaces in the context of certain $N=2$ supergravity theories, where dimensional reduction induces a mapping between {\em special} real, K\"ahler…
A Riemannian metric is termed a Hessian metric if in some coordinate system it can be locally represented as the Hessian quadratic form of some locally defined smooth potential function. Under very mild extra technical conditions, we first…
We propose studies of special Riemannian geometries with structure groups $H_1=SO(3)\subset SO(5)$, $H_2=SU(3)\subset SO(8)$, $H_3=Sp(3)\subset SO(14)$ and $H_4=F_4\subset SO(26)$ in respective dimensions 5, 8, 14 and 26. These geometries,…
Geometric algebra is a mathematical structure that is inherent in any metric vector space, and defined by the requirement that the metric tensor is given by the scalar part of the product of vectors. It provides a natural framework in which…
We study geometric structures arising from Hermitian forms on linear spaces over real algebras beyond the division ones. Our focus is on the dual numbers, the split-complex numbers, and the split-quaternions. The corresponding geometric…
We investigate the target space geometry of supersymmetric sigma models in two dimensions with Euclidean signature, and the conditions for N=2 supersymmetry. For a real action, the geometry for the N=2 model is not the generalized Kahler…
Since the end of the 19th century, and after the works of F. Klein and H. Poincar\'e, it is well known that models of elliptic geometry and hyperbolic geometry can be given using projective geometry, and that Euclidean geometry can be seen…
Isoparametric hypersurfaces and their application to special geometries
Geometric duality theory for multiple objective linear programming problems turned out to be very useful for the development of efficient algorithms to generate or approximate the whole set of nondominated points in the outcome space. This…
An introductory overview of vector spaces, algebras, and linear geometries over an arbitrary commutative field is given. Quotient spaces are emphasized and used in constructing the exterior and the symmetric algebras of a vector space.…
The notion of a complex tangent arises for embeddings of real manifolds into complex spaces. It is of particular interest when studying embeddings of real $n$-dimensional manifolds into $\mathbb{C}^n$. The generic topological structure of…
We review some basic concepts related to convex real projective structures from the differential geometry point of view. We start by recalling a Riemannian metric which originates in the study of affine spheres using the Blaschke connection…
Supersymmetric $\,\textrm{AdS}_{4}\,$, $\,\textrm{AdS}_{2} \times \Sigma_{2}\,$ and asymptotically AdS$_{4}$ black hole solutions are studied in the context of non-minimal $\,\mathcal{N}=2\,$ supergravity models involving three vector…
We construct four-dimensional domain wall solutions of N=2 gauged supergravity coupled to vector and to hypermultiplets. The gauged supergravity theories that we consider are obtained by performing two types of Abelian gauging. In both…