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Sasakian manifold

Index Sasakian manifold

In differential geometry, a Sasakian manifold (named after Shigeo Sasaki) is a contact manifold (M,\theta) equipped with a special kind of Riemannian metric g, called a Sasakian metric. [1]

15 relations: Circle bundle, Conifold, Contact geometry, Del Pezzo surface, Differential geometry, Homothetic vector field, Hyperkähler manifold, Isometry, Kähler manifold, Killing vector field, Ricci-flat manifold, Riemannian manifold, Shigeo Sasaki, String theory, Vector space.

Circle bundle

In mathematics, a circle bundle is a fiber bundle where the fiber is the circle \scriptstyle \mathbf^1.

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Conifold

In mathematics and string theory, a conifold is a generalization of a manifold.

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Contact geometry

In mathematics, contact geometry is the study of a geometric structure on smooth manifolds given by a hyperplane distribution in the tangent bundle satisfying a condition called 'complete non-integrability'.

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Del Pezzo surface

In mathematics, a del Pezzo surface or Fano surface is a two-dimensional Fano variety, in other words a non-singular projective algebraic surface with ample anticanonical divisor class.

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Differential geometry

Differential geometry is a mathematical discipline that uses the techniques of differential calculus, integral calculus, linear algebra and multilinear algebra to study problems in geometry.

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Homothetic vector field

A homothetic vector field (sometimes homothetic collineation or homothety) is a projective vector field which satisfies the condition: where c is a real constant.

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Hyperkähler manifold

In differential geometry, a hyperkähler manifold is a Riemannian manifold of dimension 4k and holonomy group contained in Sp(''k'') (here Sp(k) denotes a compact form of a symplectic group, identified with the group of quaternionic-linear unitary endomorphisms of a k-dimensional quaternionic Hermitian space).

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Isometry

In mathematics, an isometry (or congruence, or congruent transformation) is a distance-preserving transformation between metric spaces, usually assumed to be bijective.

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Kähler manifold

In mathematics and especially differential geometry, a Kähler manifold is a manifold with three mutually compatible structures: a complex structure, a Riemannian structure, and a symplectic structure.

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Killing vector field

In mathematics, a Killing vector field (often just Killing field), named after Wilhelm Killing, is a vector field on a Riemannian manifold (or pseudo-Riemannian manifold) that preserves the metric.

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Ricci-flat manifold

In mathematics, Ricci-flat manifolds are Riemannian manifolds whose Ricci curvature vanishes.

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Riemannian manifold

In differential geometry, a (smooth) Riemannian manifold or (smooth) Riemannian space (M,g) is a real, smooth manifold M equipped with an inner product g_p on the tangent space T_pM at each point p that varies smoothly from point to point in the sense that if X and Y are differentiable vector fields on M, then p \mapsto g_p(X(p),Y(p)) is a smooth function.

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Shigeo Sasaki

Shigeo Sasaki 佐々木 (18 November 1912 Yamagata Prefecture, Japan – 14 August 1987 Tokyo) was a Japanese mathematician working on differential geometry who introduced Sasaki manifolds.

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String theory

In physics, string theory is a theoretical framework in which the point-like particles of particle physics are replaced by one-dimensional objects called strings.

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Vector space

A vector space (also called a linear space) is a collection of objects called vectors, which may be added together and multiplied ("scaled") by numbers, called scalars.

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Redirects here:

Sasaki manifold, T-Sasakian manifold, T-sasakian manifold.

References

[1] https://en.wikipedia.org/wiki/Sasakian_manifold

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