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

CONFORMALMOTION OF CONTACT MANIFOLDSWITH CHARACTERISTIC VECTOR FIELD IN THEk-NULLITY DISTRIBUTION

We prove that the normal metric contact pairs with orthogonal characteristic foliations, which are either Bochner flat or locally conformally flat, are locally isometric to the Hopf manifolds. As a corollary we obtain the classification of locally conformally flat and Bochner-flat non-K\"ahler Vaisman manifolds.

Bochner and Conformal Flatness of Normal Metric Contact Pairs

In [8, 9] S. Webster showed a relation between the geometry of a Kahler manifold and the pseudo-conformal geometry of a real hypersurface in C. In particular the Bochner tensor of the Kahler manifold may be identified with the fourth order pseudo-conformal invariant of Chern and Moser [3] of a real hypersurface constructed to be a circle bundle over a neighbourhood of the Kahler manifold. It is this relation between the two geometries that we wish to study further here and we prove two results. The first is that if an infinitesimal pseudo-conformal transformation on the circle bundle of the Webster construction is projectable, the projected vector field is an infinitesimal isometry of the Kahler metric. The second theorem is that if a holomorphic transformation of a Kahler manifold preserves the Bochner tensor, its covariant derivatives and the tensor Daβ (see below), it is a homothety. It is known that the Bochner tensor is a conformal invariant [7], but of course a conformal, non-homothetic change of a Kahler metric destroys the Kahler property. Though conceivable that there may be holomorphic transformations preserving the Bochner tensor other than homotheties we conjecture not and Theorem 2 is a result in this direction.

/pdf/on-the-relation-between-pseudo-conformal-and-kahler-geometry-5ejarru6ei.pdf

On the relation between pseudo-conformal and Kahler geometry

On the space of Riemannian metrics on surfaces and contact manifolds

/pdf/umbilical-submanifolds-of-sasakian-space-forms-txz7vy2l4t.pdf

David E. Blair

Papers

CONFORMALMOTION OF CONTACT MANIFOLDSWITH CHARACTERISTIC VECTOR FIELD IN THEk-NULLITY DISTRIBUTION

Bochner and Conformal Flatness of Normal Metric Contact Pairs

On the relation between pseudo-conformal and Kahler geometry

On the space of Riemannian metrics on surfaces and contact manifolds

Umbilical submanifolds of Sasakian space forms