Recently S. Tanno has classified connected almostcontact Riemannian manifolds whose automorphism groups have themaximum dimension [9]. In his classification table the almost contactRiemannian manifolds are divided into three classes: (1) homogeneousnormal contact Riemannian manifolds with constant 0-holomorphic sec-tional curvature if the sectional curvature for 2-planes which contain

/pdf/a-class-of-almost-contact-riemannian-manifolds-1yxyggdui1.pdf

A class of almost contact riemannian manifolds

Certain conditions for a Riemannian manifold to be isometric with a sphere:Dedicated to Professor Kentaro Yano on his fiftieth birthday

We give a description of all complete simply connected Riemannian manifolds carrying real Killing spinors. Furthermore, we present a construction method for manifolds with the exceptional holonomy groupsG
2 and Spin(7).

https://projecteuclid.org/download/pdf_1/euclid.cmp/1104253076

Real Killing spinors and holonomy

http://www.dcs.gla.ac.uk/~muffy/papers/calder-kolberg-magill-reiff.pdf

Feature interaction: a critical review and considered forecast

We analyse the geometrical structure of supersymmetric solutions of type II supergravity of the form Open image in new window1,9−n×Mn with non-trivial NS flux and dilaton. Solutions of this type arise naturally as the near-horizon limits of wrapped NS fivebrane geometries. We concentrate on the case d=7, preserving two or four supersymmetries, corresponding to branes wrapped on associative or SLAG three-cycles. Given the existence of Killing spinors, we show that M7 admits a G2-structure or an SU(3)-structure, respectively, of specific type. We also prove the converse result. We use the existence of these geometric structures as a new technique to derive some known and new explicit solutions, as well as a simple theorem implying that we have vanishing NS three-form and constant dilaton whenever M7 is compact with no boundary. The analysis extends simply to other type II examples and also to type I supergravity.

G-Structures and Wrapped NS5-Branes

/pdf/generalization-of-myers-theorem-on-a-contact-manifold-9122yw9obs.pdf

Generalization of Myers' Theorem on a contact manifold

We study contact metric and trans-Sasakian generalized Sasakian-space-forms. We also give some interesting examples of generalized Sasakian-space-forms by using warped products and conformal changes of metric.

/pdf/on-generalized-sasakian-space-forms-3uwtw9m5ig.pdf

On generalized Sasakian-space-forms

/pdf/hypersurfaces-of-odd-dimensional-spheres-30phbhchaa.pdf

Hypersurfaces of odd-dimensional spheres

We will prove that normal complex contact metric manifolds that are Bochner flat must have constant holomorphic sectional curvature 4 and be Kahler. If they are also complete and simply connected, they must be isometric to the odd-dimensional complex projective space $${{\mathbb{C}P^{2n+1}}}$$
 (4) with the Fubini-Study metric. On the other hand, it is not possible for normal complex contact metric manifolds to be conformally flat.

/pdf/bochner-and-conformal-flatness-on-normal-complex-contact-1hygcc1u94.pdf

Bochner and conformal flatness on normal complex contact metric manifolds

https://projecteuclid.org/download/pdf_1/euclid.kmj/1138847256

David E. Blair

Papers

Generalization of Myers' Theorem on a contact manifold

On generalized Sasakian-space-forms

Hypersurfaces of odd-dimensional spheres

Bochner and conformal flatness on normal complex contact metric manifolds

Semi-invariant immersions