Classification of Riemannian Manifolds in Conformally Invariant Potential Theory

2020 ◽  
pp. 237-247
Author(s):  
Ilkka Holopainen ◽  
Seppo Rickman
Keyword(s):  
Potential Theory ◽  
Riemannian Manifolds ◽  
Conformally Invariant ◽  
Invariant Potential

scholarly journals The even Clifford structure of the fourth Severi variety

2015 ◽  
Vol 2 (1) ◽  
Author(s):  
Maurizio Parton ◽  
Paolo Piccinni
Keyword(s):  
Vector Bundle ◽  
Riemannian Manifolds ◽  
Severi Variety ◽  
Simply Connected

AbstractTheHermitian symmetric spaceM = EIII appears in the classification of complete simply connected Riemannian manifolds carrying a parallel even Clifford structure [19]. This means the existence of a real oriented Euclidean vector bundle E over it together with an algebra bundle morphism φ : Cl

scholarly journals CONFORMAL SUPERFIELDS AND BPS STATES IN AdS4/7 GEOMETRIES

2000 ◽  
Vol 14 (22n23) ◽  
pp. 2315-2333 ◽  
Author(s):  
SERGIO FERRARA ◽  
EMERY SOKATCHEV
Keyword(s):  
Black Holes ◽  
De Sitter ◽  
Harmonic Superspace ◽  
Supergravity Theory ◽  
Conformally Invariant ◽  
Highest Weight ◽  
Ads Black Holes ◽  
Different Types ◽  
Bps States

We carry out a general analysis of the representations of the superconformal algebras OSp(8/4, ℝ) and OSp(8*/2N) in terms of harmonic superspace. We present a construction of their highest-weight UIR's by multiplication of the different types of massless conformal superfields ("supersingletons"). Particular attention is paid to the so-called "short multiplets". Representations undergoing shortening have "protected dimension" and may correspond to BPS states in the dual supergravity theory in anti-de Sitter space. These results are relevant for the classification of multitrace operators in boundary conformally invariant theories as well as for the classification of AdS black holes preserving different fractions of supersymmetry.

scholarly journals Classification of Ricci solitons on Euclidean hypersurfaces

2014 ◽  
Vol 25 (11) ◽  
pp. 1450104 ◽  
Author(s):  
Bang-Yen Chen ◽  
Sharief Deshmukh
Keyword(s):  
Riemannian Manifold ◽  
Vector Field ◽  
Riemannian Manifolds ◽  
Potential Field ◽  
Vector Fields ◽  
Ricci Soliton ◽  
Position Vector ◽  
Ricci Solitons ◽  
Euclidean Submanifolds

A Ricci soliton (M, g, v, λ) on a Riemannian manifold (M, g) is said to have concurrent potential field if its potential field v is a concurrent vector field. Ricci solitons arisen from concurrent vector fields on Riemannian manifolds were studied recently in [Ricci solitons and concurrent vector fields, preprint (2014), arXiv:1407.2790]. The most important concurrent vector field is the position vector field on Euclidean submanifolds. In this paper we completely classify Ricci solitons on Euclidean hypersurfaces arisen from the position vector field of the hypersurfaces.

scholarly journals REPRESENTATIONS OF SUPERCONFORMAL ALGEBRAS IN THE AdS7/4/CFT6/3 CORRESPONDENCE

2001 ◽  
Vol 16 (05) ◽  
pp. 976-989 ◽  
Author(s):  
SERGIO FERRARA ◽  
EMERY SOKATCHEV
Keyword(s):  
Black Holes ◽  
De Sitter ◽  
Harmonic Superspace ◽  
Supergravity Theory ◽  
Conformally Invariant ◽  
Highest Weight ◽  
Ads Black Holes ◽  
Different Types ◽  
Bps States

We perform a general analysis of representations of the superconformal algebras OSp (8/4, ℝ) and OSp (8*/2N) in harmonic superspace. We present a construction of their highest-weight UIR's by multiplication of the different types of massless conformal superfields ("supersingletons"). In particular, all "short multiplets" are classified. Representations undergoing shortening have "protected dimension" and may correspond to BPS states in the dual supergravity theory in anti-de Sitter space. These results are relevant for the classification of multitrace operators in boundary conformally invariant theories as well as for the classification of AdS black holes preserving different fractions of supersymmetry.

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