A decomposition theorem on Euclidean Steiner minimal trees

F. K. Hwang; G. D. Song; G. Y. Ting; D. Z. Du

doi:10.1007/bf02187919

A decomposition theorem on Euclidean Steiner minimal trees

Discrete & Computational Geometry ◽

10.1007/bf02187919 ◽

1988 ◽

Vol 3 (4) ◽

pp. 367-382 ◽

Cited By ~ 12

Author(s):

F. K. Hwang ◽

G. D. Song ◽

G. Y. Ting ◽

D. Z. Du

Keyword(s):

Decomposition Theorem ◽

Steiner Minimal Trees

Download Full-text

Some remarks on the Balog–Wooley decomposition theorem and quantities D +, D ×

Proceedings of the Steklov Institute of Mathematics ◽

10.1134/s0081543817070057 ◽

2017 ◽

Vol 298 (S1) ◽

pp. 74-90 ◽

Cited By ~ 1

Author(s):

I. D. Shkredov

Keyword(s):

Decomposition Theorem

Download Full-text

Polynomial identities related to special Schubert varieties

Applicable Algebra in Engineering Communication and Computing ◽

10.1007/s00200-021-00496-6 ◽

2021 ◽

Author(s):

Francesca Cioffi ◽

Davide Franco ◽

Carmine Sessa

Keyword(s):

Arbitrary Number ◽

Schubert Variety ◽

Decomposition Theorem ◽

Point Of View ◽

Explicit Description ◽

Intersection Cohomology ◽

Schubert Varieties ◽

Polynomial Identities ◽

Poincaré Polynomial

AbstractLet $$\mathcal S$$ S be a single condition Schubert variety with an arbitrary number of strata. Recently, an explicit description of the summands involved in the decomposition theorem applied to such a variety has been obtained in a paper of the second author. Starting from this result, we provide an explicit description of the Poincaré polynomial of the intersection cohomology of $$\mathcal S$$ S by means of the Poincaré polynomials of its strata, obtaining interesting polynomial identities relating Poincaré polynomials of several Grassmannians, both by a local and by a global point of view. We also present a symbolic study of a particular case of these identities.

Download Full-text

Curvature of quaternionic Kähler manifolds with $$S^1$$-symmetry

manuscripta mathematica ◽

10.1007/s00229-021-01294-7 ◽

2021 ◽

Author(s):

V. Cortés ◽

A. Saha ◽

D. Thung

Keyword(s):

Curvature Tensor ◽

Decomposition Theorem ◽

Kähler Manifolds ◽

Kahler Manifolds ◽

Riemann Curvature ◽

Riemann Curvature Tensor ◽

Cohomogeneity One ◽

Civita Connection ◽

Levi Civita Connection ◽

Quaternionic Kähler

AbstractWe study the behavior of connections and curvature under the HK/QK correspondence, proving simple formulae expressing the Levi-Civita connection and Riemann curvature tensor on the quaternionic Kähler side in terms of the initial hyper-Kähler data. Our curvature formula refines a well-known decomposition theorem due to Alekseevsky. As an application, we compute the norm of the curvature tensor for a series of complete quaternionic Kähler manifolds arising from flat hyper-Kähler manifolds. We use this to deduce that these manifolds are of cohomogeneity one.

Download Full-text