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

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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

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On intrinsic structures similar to those induced on S2n

/pdf/hypersurface-of-an-even-dimensional-sphere-satisfying-a-45298xbjpe.pdf

Hypersurface of an even-dimensional sphere satisfying a certain commutative condition

In this paper, we first focus on conformally flat almost $${C(\alpha)}$$
 -manifolds. Moreover, we construct an example of a 3-dimensional conformally flat almost $${\alpha}$$
 -Kenmotsu manifold which is of non-constant sectional curvature. By means of this example, we also illustrate a 3-dimensional conformally flat almost Kenmotsu manifold which not only contrasts with both H
 3(−1) and $${H^{2}(-4)\times\mathbb{R}}$$
 but also is of non-constant sectional curvature. Then, we study conformally flat, $${\phi}$$
 -RK contact metric and almost contact metric manifolds. Next, we investigate the curvature properties of conformally flat generalized Sasakian space forms. Finally, we deal with conformally flat almost contact metric manifolds which are *-
 $${\eta}$$
 -Einstein. In this regard, we are also interested in conformally flat contact metric manifolds of $${{\rm dim}{\geq}5}$$
 which are *-
 $${\eta}$$
 -Einstein.

https://link.springer.com/content/pdf/10.1007%2Fs00009-015-0652-x.pdf

On Conformally Flat Almost Contact Metric Manifolds

https://projecteuclid.org/download/pdf_1/euclid.tjm/1270130378

2-Type Integral Surfaces in $S^5(1)$

https://www.cambridge.org/core/services/aop-cambridge-core/content/view/S0308210500010994

David E. Blair

Papers

On intrinsic structures similar to those induced on S2n

Hypersurface of an even-dimensional sphere satisfying a certain commutative condition

On Conformally Flat Almost Contact Metric Manifolds

2-Type Integral Surfaces in $S^5(1)$

On the non-regularity of tangent sphere bundles