The Kempf–Ness Theorem and invariant theory for real reductive representations

Biliotti, Leonardo

doi:10.1007/s40863-019-00151-6

Cited by 2 publications

(2 citation statements)

References 40 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Proof. It is well-known that V , respectively W , is U C -semistable, respectively G-semistable [17], see also [4]. Since W is a Lagrangian subspace of V , applying the above Proposition the result follows.…”

Section: Norm Square Of the Gradient Mapmentioning

confidence: 71%

A splitting result for real submanifolds of a Kahler manifold

Biliotti¹

2021

Preprint

Self Cite

View full text Add to dashboard Cite

Let (Z, ω) be a connected Kähler manifold with an holomorphic action of the complex reductive Lie group U C , where U is a compact connected Lie group acting in a hamiltonian fashion. Let G be a closed compatible Lie group of U C and let M be a G-invariant connected submanifold ofThe vice-versa is also investigated. We also characterize G-invariant real submanifolds such that the norm square of the gradient map is constant. As an application, we prove a splitting result for real connected submanifolds of (Z, ω) generalizing a result proved in [7], see also [1,3].

show abstract

Section: Norm Square Of the Gradient Mapmentioning

confidence: 71%

A splitting result for real submanifolds of a Kahler manifold

Biliotti¹

2021

Preprint

Self Cite

View full text Add to dashboard Cite

show abstract

“…Corollary 13 Let G be a real form of U . Let V be complex vector space and W be real (Richardson and Slodowoy 1990), see also Biliotti (2021). Since W is a Lagrangian subspace of V , applying the above Proposition it follows that G (Borel and Harish-Chandra 1962, Proposition 2.3).…”

Section: Note Also That Kmentioning

confidence: 96%

A Splitting Result for Real Submanifolds of a Kähler Manifold

Biliotti

2021

Bull Braz Math Soc, New Series

Self Cite

View full text Add to dashboard Cite

Let $$(Z,\omega )$$ ( Z , ω ) be a connected Kähler manifold with an holomorphic action of the complex reductive Lie group $$U^\mathbb {C}$$ U C , where U is a compact connected Lie group acting in a hamiltonian fashion. Let G be a closed compatible Lie group of $$U^\mathbb {C}$$ U C and let M be a G-invariant connected submanifold of Z. Let $$x\in M$$ x ∈ M . If G is a real form of $$U^\mathbb {C}$$ U C , we investigate conditions such that $$G\cdot x$$ G · x compact implies $$U^\mathbb {C}\cdot x$$ U C · x is compact as well. The vice-versa is also investigated. We also characterize G-invariant real submanifolds such that the norm-square of the gradient map is constant. As an application, we prove a splitting result for real connected submanifolds of $$(Z,\omega )$$ ( Z , ω ) generalizing a result proved in Gori and Podestà (Ann Global Anal Geom 26: 315–318, 2004), see also Bedulli and Gori (Results Math 47: 194–198, 2005), Biliotti (Bull Belg Math Soc Simon Stevin 16: 107–116 2009).

show abstract

The Kempf–Ness Theorem and invariant theory for real reductive representations

Abstract: This paper does not contain any new result. We give new proofs of the Kempf-Ness Theorem and Hilbert-Mumford criterion for real reductive representations avoiding any algebraic results.

Cited by 2 publications

References 40 publications

A splitting result for real submanifolds of a Kahler manifold

A splitting result for real submanifolds of a Kahler manifold

A Splitting Result for Real Submanifolds of a Kähler Manifold

Contact Info

Product

Resources

About