Suppose that an algebraic torus G acts algebraically on a projective manifold X with generically trivial stabilizers. Then the Zariski closure of the set of pairs {(x, y) ∈ X × X | y = gx for some g ∈ G} defines a nonzero equivariant cohomology class [∆G] ∈ H G×G(X×X). We give an analogue of this construction in the case where X is a compact symplectic manifold endowed with a hamiltonian action...

The 1-skeleton of a G-manifold M is the set of points p ∈ M , where dimGp ≥ dimG − 1, and M is a GKM manifold if the dimension of this 1-skeleton is 2. M. Goresky, R. Kottwitz, and R. MacPherson show that for such a manifold this 1-skeleton has the structure of a “labeled” graph, ( , α), and that the equivariant cohomology ring ofM is isomorphic to the “cohomology ring” of this graph. Hence, if...

We show that the moduli spaces of associative submanifolds of a G 2 manifold (and Cayley submanifolds of a Spin(7) manifold) can be perturbed to smooth manifolds. By using connections as natural parameters and by constraining them with an additional equation and using Seiberg-Witten theory we can make them compact, and hence assign local invariants to these submanifolds. The local equations of ...

We produce new examples of harmonic maps, having as either source or target manifold the tangent bundle TM on a Riemannian manifold (M,g), equipped with a Riemannian g-natural metric G. In particular, we study the harmonicity of the canonical projection π : (TM,G)→ (M,g), and of the identity map (TM,G)→ (TM,gS) and conversely, gS being the Sasaki metric on TM. A corresponding study is made for ...

Scores on cognitive tasks used in intelligence tests correlate positively with each other, that is, they display a positive manifold of correlations. The positive manifold is often explained by positing a dominant latent variable, the g factor, associated with a single quantitative cognitive or biological process or capacity. In this article, a new explanation of the positive manifold based on ...

Given a smooth free action of compact connected Lie group $G$ on manifold $M$, we show that the space $G$-invariant Riemannian metrics $M$ whose automorphism is precisely open dense in all metrics, provided dimension "sufficiently large" compared to $G$. As consequence, it follows every can be realized as some manifold; this recovers prior work by Bedford-Dadok and Saerens-Zame under less strin...

The present article serves the purpose of pursuing Geometrization of heat flow on volumetrically isothermal manifold by means of RF approach. In this article, we have analyzed the evolution of heat equation in a 3-dimensional smooth isothermal manifold bearing characteristics of Riemannian manifold and fundamental properties of thermodynamic systems. By making use of the notions of various curva...

We study the properties of Ricci curvature ${\mathfrak{g}}$-manifolds with particular attention paid to higher dimensional abelian Lie algebra case. The relations between manifold and transverse characteristic foliation are investigated. In particular, sufficient conditions found under which ${\mathfrak{g}}$-manifold can be a soliton or gradient soliton. Finally, we obtain amazing (non-existenc...

In this note, we explain how a well-known construction of isospectral manifolds leads to an obstruction to a group being the fundamental group of a closed 3-dimensional manifold. The problem of determining, for a given group G, whether there is a closed 3-manifold M with π1(M) ∼= G is readily seen to be undecidable; let us write G ∈ G 3 if there is such a 3-manifold. A standard conjecture (rela...

In this paper, we obtain a necessary and sufficient condition for a conformal mapping between two Weyl manifolds to preserve Einstein tensor. Then we prove that some basic curvature tensors of $W_n$ are preserved by such a conformal mapping if and only if the covector field of the mapping is locally a gradient. Also, we obtained the relation between the scalar curvatures of the Weyl manifolds r...