Riemannian Geometry of Contact and Symplectic Manifolds

By D. Blair. 2002

2,353 citations recorded by the source corpus.

Subfields: Applied Mathematics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/507a33b0586eb133ca0bcfc25aefc071020e99a0

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In Applied Mathematics

In Geometry and Topology

Citations in the corpus

Almost Ricci solitons and $$K$$K-contact geometry (2014, neutral): “(16) For details we refer to [4].”
Ricci solitons on 3-dimensional cosymplectic manifolds (2017, methodology): “By Blair [1], the normality of an almost contact structure is expressed by [φ, φ] = −2dη ⊗ ξ, where [φ, φ] denotes the Nijenhuis tensor of φ.”
On slant curves in Sasakian 3-manifolds (2006, neutral): “Our general reference is [3].”
Canonical connections on paracontact manifolds (2007, background): “ paracomplex structure is called paracomplex or integrable. An immediate consequence of the denition of the almost paracontact structure is that the endomorphism ’has rank 2n, ’˘= 0 and ’= 0, (see [1, 2] for the almost contact case). If a manifold M(2n+1) with (’;˘;)-structure admits a pseudo-Rieman”
A Canonical Compatible Metric for Geometric Structures on Nilmanifolds (2004, background): “For a compact simple Lie group, −B is minimal for the case = 0, and if g = k ⊕ p is the Cartan decomposition for a non-compact semi-simple Lie algebra g, then it is easy to see that the metric h� , �i given by h k, pi = 0, h� , �i| k× k = −B and h� , �i| p×p = B is minimal as well.”
Twisted supersymmetric 5D Yang-Mills theory and contact geometry (2012, background): “For the proof of the existence of a compatible metric and other related properties the reader may consult the textbook [23].”
Generalized Sasakian-space-forms (2004, background): “For more background on almost contact metric manifolds, we recommend the reference [3].”
Contact pseudo-metric manifolds (2010, methodology): “If we consider the diffeomorphism f : R3 → R3, (x, y, z) → (x1, x2, x3) = (z cos x − y sin x,−z sin x − y cos x,−x), then ( f −1)∗η = η0 and ( f −1)∗ g0 = ḡ0R , where η0 = (1)2 (cos x3 dx1 + sin x3 dx2) and ḡ0R = (1)4 ∑ i dx 2 i [4].”
Certain Contact Metrics as Ricci Almost Solitons (2014, methodology): “On a K-contact manifold the following formulas are known [4] ∇Xξ = −φX, (2.”
Almost Kenmotsu manifolds and local symmetry (2007, methodology): “For more details, we refer to Blair’s books [3], [5].”
Almost Kenmotsu Manifolds and Nullity Distributions (2009, methodology): “For more details, we refer to Blair’s books [3, 4 ]. A Kenmotsu manifold can be defined as a normal almost contact metric manifold such that dη =0 andd Φ=2 η ∧ Φ. Vol.”
Contact metric manifolds with η-parallel torsion tensor (2008, methodology): “Following Blair [ 1 ] we define two self-adjoint operators h and l (the Jacobi operator with respect to ξ )b yh = 1 (£ξ ϕ)and l = R(., ξ )ξ, respectively.”
∗-Ricci solitons and gradient almost ∗-Ricci solitons on Kenmotsu manifolds (2019, background): “ell known that a (2n+1) dimensional smooth manifold M admits an almost contact structure if and only if the structure group of the tangent bundle of M reduces to U(n)×1. For more details, we refer to [1]. If M with (ϕ,ξ,η)-structure admits a Riemannian metric g such that g(ϕX,ϕY) = g(X,Y) − η(X)η(Y ”