Related papers: A new Ricci flat geometry
We introduce the notions of `super-Ricci flows' and `Ricci flows' for time-dependent families of metric measure spaces $(X,d_t,m_t)_{t\in I}$. The former property is proven to be stable under suitable space-time versions of mGH-convergence.…
A theorem of differential geometry is employed to locally embed a wide class of superstring backgrounds that admit a covariantly constant null Killing vector field in eleven-dimensional, Ricci-flat spaces. Included in this class are exact…
We prove that there exists a gradient expanding Ricci soliton asymptotic to any given cone over the product of a round sphere and a Ricci flat manifold. In particular we obtain asymptotically conical expanding Ricci solitons with positive…
In the previous work we introduced a new static cylindrically symmetric vacuum solutions in Weyl coordinates in the context of the metric f(R) theories of gravity\cite{1}. Now we obtain a 2-parameter family of exact solutions which contains…
We give a global picture of the Ricci flow on the space of three-dimensional, unimodular, nonabelian metric Lie algebras considered up to isometry and scaling. The Ricci flow is viewed as a two-dimensional dynamical system for the evolution…
We analyze the transverse K\"{a}hler-Ricci flow equation on Sasaki-Ein\-stein space $Y^{p,q}$. Explicit solutions are produced representing new five-dimensional Sasaki structures. Solutions which do not modify the transverse metric preserve…
An explicit one-parameter Lie point symmetry of the four-dimensional vacuum Einstein equations with two commuting hypersurface-orthogonal Killing vector fields is presented. The parameter takes values over all of the real line and the…
Spherical symmetry in $f(R)$ gravity is discussed in details considering also the relations with the weak field limit. Exact solutions are obtained for constant Ricci curvature scalar and for Ricci scalar depending on the radial coordinate.…
Classical gravitating field theories reduced to three dimensions admit manifest gauge invariances and hidden symmetries, which together make up the invariance group G of the theory. If this group is large enough, the target space is a…
We construct supergravity solutions describing the near horizon limit of D1D5 systems with non-trivial boundary conditions. Upon reduction to five dimensions they define Melvin universes with NS--NS/RR fluxes, that smoothly interpolate…
In this paper we investigate the possibility to obtain locally new Sasaki-Einstein metrics on the space $T^{1,1}$ considering a deformation of the standard metric tensor field. We show that from the geometric point of view this deformation…
We propose a closed formula of the universal part of supersymmetric R\'enyi entropy $S_q$ for $(2,0)$ superconformal theories in six-dimensions. We show that $S_q$ across a spherical entangling surface is a cubic polynomial of…
In a recent paper, we have pointed out a relation between the Killing spinor and Einstein equations. Using this relation, new brane solutions of D=11 and D=10 type IIB supergravity theories are constructed. It is shown that in a brane…
We prove the existence of Ricci flow starting from a class of metrics with unbounded curvature, which are doubly-warped products over an interval with a spherical factor pinched off at an end. These provide a forward evolution from some…
We have found the solution to the back reaction of putting a stack of coincident D3 and D5 branes in $R^{3,1}\times M_6$, where $M_6$ is constructed from an infinite class of Sasaki-Einstein spaces, $L^{(p,q,r)}$. The non-zero fluxes…
We study several questions involving relative Ricci-flat K\"ahler metrics for families of log Calabi-Yau manifolds. Our main result states that if $p:(X,B)\to Y$ is a K\"ahler fiber space such that $\displaystyle (X_y, B|_{X_y})$ is…
Motivated by the long-time behavior of Ricci flows that collapse with bounded curvature, we study expanding Ricci solitons with nilpotent symmetry on vector bundles over a closed manifold. We prove that, under mild assumptions that are…
By combining the join construction from Sasakian geometry with the Hamiltonian 2-form construction from K\"ahler geometry, we recover Sasaki-Einstein metrics discovered by physicists. Our geometrical approach allows us to give an algorithm…
In this paper we generalize electric S-brane solutions with maximal number of branes. Previously for the action containing D-dimensional gravity, a scalar field and antisymmetric (p+2)-form we found composite, electric S-brane solutions…
In this work we construct and analyze exact solutions describing Ricci flows and nonholonomic deformations of four dimensional (4D) Taub-NUT spacetimes. It is outlined a new geometric techniques of constructing Ricci flow solutions. Some…