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