In this paper we develop a relative version of T-duality in generalized complex geometry which we propose as a manifestation of mirror symmetry. Let M be an n−dimensional smooth real manifold, V a rank n real vector bundle on M , and ∇ a flat connection on V . We define the notion of a ∇−semi-flat generalized complex structure on the total space of V . We show that there is an explicit bijectiv...

We study a class of asymptotically cylindrical Ricci-flat Kähler metrics arising on quasiprojective manifolds. Using the Calabi–Yau geometry and analysis and the Kodaira–Kuranishi–Spencer theory and building up on results of N.Koiso, we show that under rather general hypotheses any local asymptotically cylindrical Ricci-flat deformations of such metrics are again Kähler, possibly with respect t...

We prove non–existence of static, vacuum, appropriately regular, asymptotically flat black hole space–times with degenerate (not necessarily connected) components of the event horizon. This finishes the classification of static, vacuum, asymptotically flat domains of outer communication in an appropriate class of space–times, showing that the domains of outer communication of the Schwarzschild ...

We compute the Riemannian volume of the moduli space of flat connections on a nonorientable 2-manifold, for a natural class of metrics. We also show that Witten’s volume formula for these moduli spaces may be derived using Haar measure, and we give a new proof of Witten’s volume formula for the moduli space of flat connections on a Riemann surface using Haar measure. ———————–

Kinematic and geometrical aspects of the connection between energy and inertial mass are considered. Transformations of coordinate and time are obtained in a two-dimensional flat space. For this case the Euclidean, pseudo-Euclidean and Galilean kinematics are considered. A new interval in a flat fourdimensional anisotropic Finsler space is found. Under certain assumptions the known results foll...

A construction of conformal infinity in null and spatial directions is constructed for the Rainbow-flat space-time corresponding to doubly special relativity. From this construction a definition of asymptotic DSRness is put forward which is compatible with the correspondence principle of Rainbow Gravity. Furthermore a result equating asymptotically flat space-times with asymptotically DSR space...

Heat sinks are used in industrial equipment to dissipate the excess heat from their heat-generating parts to the ambient. In the last few years, efforts on manufacturing electronic or mechanical devices with less weight, space, and lower cost were spent. Heat dissipation from the heat sink is stalling a big problem which many researchers are trying to solve. The aim of this study is to brief th...

There is a theorem known as a Virial theorem that restricts the possible existence of non-trivial static solitary waves with scalar fields in a flat space-time with 3 or more spatial dimensions. This raises the following question: Does the analogous curved space-time version hold?. We investigate the possibility of solitons in a 4-D curved space-time with a simple model using numerical analysis...

Only when space is flat does there exist one coordinate system which has direct meaning of distances or angles, and if one coordinate system has direct meaning of distances or angles then the space must be flat. This is the famous Riemann theorem when he pioneered the concept of curved space. General relativity (GR) claims curved spacetime. However, when testing GR with data, all relativists co...

‎we call a ring $r$ right generalized semiperfect if every simple right $r$-module is an epimorphic image of a flat right $r$-module with small kernel‎, ‎that is‎, ‎every simple right $r$-module has a flat $b$-cover‎. ‎we give some properties of such rings along with examples‎. ‎we introduce flat strong covers as flat covers which are also flat $b$-covers and give characterizations of $a$-perfe...