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Что (кто) такое extremal curvature - определение

POINT AT A DISTANCE FROM THE CURVE EQUAL TO THE RADIUS OF CURVATURE LYING ON THE NORMAL VECTOR

Center of Curvature; Centre of curvature

Ricci curvature

2-TENSOR OBTAINED AS A CONTRACTION OF THE RIEMAN CURVATURE 4-TENSOR ON A RIEMANNIAN MANIFOLD (OR, MORE GENERALLY, A SMOOTH MANIFOLD EQUIPPED WITH AFFINE CONNECTION)

Ricci-curvature; Ricci curvature tensor; Ricci tensor; Trace-free Ricci tensor; Ricci form; Ricci Curvature

In differential geometry, the Ricci curvature tensor, named after Gregorio Ricci-Curbastro, is a geometric object which is determined by a choice of Riemannian or pseudo-Riemannian metric on a manifold. It can be considered, broadly, as a measure of the degree to which the geometry of a given metric tensor differs locally from that of ordinary Euclidean space or pseudo-Euclidean space.

https://en.wikipedia.org/wiki/Ricci_curvature

Radius of curvature

RADIUS OF A CIRCLE WHICH BEST APPROXIMATES A CURVE IN A GIVEN POINT

Radius of curvature (applications); Radius of curvature (mathematics)

In differential geometry, the radius of curvature, , is the reciprocal of the curvature. For a curve, it equals the radius of the circular arc which best approximates the curve at that point.

https://en.wikipedia.org/wiki/Radius_of_curvature

Constant scalar curvature Kähler metric

KÄHLER MANIFOLD WHOSE SCALAR CURVATURE IS CONSTANT

CscK manifold; CscK metric; CscK; Constant scalar curvature Kahler metric; Constant scalar curvature Kaehler metric; Constant scalar curvature Kähler manifold; Constant scalar curvature Kahler manifold; Extremal Kähler metric; Holomorphy potential

In differential geometry, a constant scalar curvature Kähler metric (cscK metric), is (as the name suggests) a Kähler metric on a complex manifold whose scalar curvature is constant. A special case is Kähler–Einstein metric, and a more general case is extremal Kähler metric.

https://en.wikipedia.org/wiki/Constant_scalar_curvature_Kähler_metric

Википедия

Center of curvature

In geometry, the center of curvature of a curve is found at a point that is at a distance from the curve equal to the radius of curvature lying on the normal vector. It is the point at infinity if the curvature is zero. The osculating circle to the curve is centered at the centre of curvature. Cauchy defined the center of curvature C as the intersection point of two infinitely close normal lines to the curve. The locus of centers of curvature for each point on the curve comprise the evolute of the curve. This term is generally used in physics regarding the study of lenses and mirrors (see radius of curvature (optics)).

It can also be defined as the spherical distance between the point at which all the rays falling on a lens or mirror either seems to converge to (in the case of convex lenses and concave mirrors) or diverge from (in the case of concave lenses or convex mirrors) and the lens/mirror itself.

https://en.wikipedia.org/wiki/Center of curvature