In this paper,  the concept of fuzzy metric-like spaces is introduced which generalizes  the notion of fuzzy metric spaces given by George and Veeramani cite{Vee1}. Some fixed point results for fuzzy contractive mappings on fuzzy metric-like spaces are derived. These results generalize several comparable results from the current literature. We also provide illustrative examples in support of ou...

We construct a natural L-metric on the perturbed Seiberg-Witten moduli spaces Mμ+ of a compact 4-manifold M , and we study the resulting Riemannian geometry of Mμ+ . We derive a formula which expresses the sectional curvature of Mμ+ in terms of the Green operators of the deformation complex of the Seiberg-Witten equations. In case M is simply connected, we construct a Riemannian metric on the S...

Let M be a 2n dimensional smooth closed oriented manifold. Let g be a Riemmian metric on TM and ∇ the associated Levi-Civita connection. Let V be a complex vector bundle over M with a Hermitian metric h and a unitary connection ∇ . Let ΛC(T ∗M) be the complexified exterior algebra bundle of TM and let 〈 , 〉ΛC(T∗M) be the Hermitian metric on ΛC(T ∗M) induced by g . Let dv be the Riemannian volum...

Let X be a Kähler manifold of complex dimension n with smooth Kähler metric ω, and Z ⊂ X a smooth complex hypersurface. Let L→ X be a holomorphic line bundle with a possibly singular Hermitian metric e−φ whose singular locus does not lie in Z, i.e., such that e|Z is a metric for L|Z . Assume also that the line bundle EZ → X associated to the divisor Z has a holomorphic section fZ such that Z = ...

We study Hermitian metrics with a Gauduchon connection being "K\"ahler-like", namely, satisfying the same symmetries for curvature as Levi-Civita and Chern connections. In particular, we investigate $6$-dimensional solvmanifolds invariant complex structures trivial canonical bundle metrics. The results this case give evidence two conjectures that are expected to hold in more generality: first, ...

We assume that the manifold with boundary, X, has a SpinC-structure with spinor bundle S /. Along the boundary, this structure agrees with the structure defined by an infinite order integrable almost complex structure and the metric is Kähler. In this case the SpinC-Dirac operator ð agrees with ∂̄ + ∂̄∗ along the boundary. The induced CR-structure on bX is integrable and either strictly pseudocon...

In this article, we present some results concerning the harmonicity on tangent bundle equipped with vertical rescaled metric. We establish necessary and sufficient conditions under which a vector field is harmonic respect to metric construct examples of fields. also study along map between Riemannian manifolds, target manifold its bundle. Next discuss composition projection from into another ma...

Let (M, F) be a closed foliated manifold, dimM = n, dimF = p, p+q = n, equipped with a Riemannian metric gM . We assume that the foliation F is Riemannian, and the metric gM is bundle-like. Let F = TF be the integrable distribution of tangent p-planes to F , and H = F⊥ be the orthogonal complement to F . The decomposition of TM into a direct sum, TM = F ⊕ H , induces a decomposition of the metr...

We consider a compact manifold X whose boundary is a locally trivial fiber bundle, and an associated pseudodifferential algebra that models fibered cusps at infinity. Using trace-like functionals that generate the 0-dimensional Hochschild cohomology groups we first express the index of a fully elliptic fibered cusp operator as the sum of a local contribution from the interior of X and a term th...

The total space of the tangent bundle of a Kähler manifold admits a canonical Kähler structure. Parallel translation identifies the space T of oriented affine lines in R with the tangent bundle of S. Thus, the round metric on S induces a Kähler structure on T which turns out to have a metric of neutral signature. It is shown that the isometry group of this metric is isomorphic to the isometry g...