Sign in
Author

Conference

Journal

Organization

Year

DOI
Look for results that meet for the following criteria:
since
equal to
before
between
and
Search in all fields of study
Limit my searches in the following fields of study
Agriculture Science
Arts & Humanities
Biology
Chemistry
Computer Science
Economics & Business
Engineering
Environmental Sciences
Geosciences
Material Science
Mathematics
Medicine
Physics
Social Science
Multidisciplinary
Keywords
(9)
Differential Operators
Dirac Operator
Eigenvalue Estimate
Geometric Model
Homogeneous Space
riemannian manifold
String Theory
Symmetric Space
First Order
Related Publications
(2)
Parallel spinors and connections with skewsymmetric torsion in string theory
A cubic Dirac operator and the emergence of Euler number multiplets of representations for equal rank subgroups
Subscribe
Academic
Publications
Connections on Naturally Reductive Spaces, Their Dirac Operator and Homogeneous Models in String Theory
Connections on Naturally Reductive Spaces, Their Dirac Operator and Homogeneous Models in String Theory,10.1007/s002200020743y,Communications in Ma
Edit
Connections on Naturally Reductive Spaces, Their Dirac Operator and Homogeneous Models in String Theory
(
Citations: 15
)
BibTex

RIS

RefWorks
Download
Ilka Agricola
: Given a reductive
homogeneous space
M=G/H endowed with a naturally reductive metric, we study the oneparameter family of connections ∇ t joining the canonical and the LeviCivita connection (t=0, 1/2). We show that the
Dirac operator
D t corresponding to t=1/3 is the socalled ``cubic''
Dirac operator
recently introduced by B. Kostant, and derive the formula for its square for any t, thus generalizing the classical Parthasarathy formula on symmetric spaces. Applications include the existence of a new Ginvariant
first order
differential operator on spinors and an
eigenvalue estimate
for the first eigenvalue of D 1/3. This geometric situation can be used for constructing Riemannian manifolds which are Ricci flat and admit a parallel spinor with respect to some metric connection ∇ whose torsion T≠ 0 is a 3form, the
geometric model
for the common sector of string theories. We present some results about solutions to the string equations and a detailed discussion of a 5dimensional example.
Journal:
Communications in Mathematical Physics  COMMUN MATH PHYS
, vol. 232, no. 3, pp. 535563, 2003
DOI:
10.1007/s002200020743y
Cumulative
Annual
View Publication
The following links allow you to view full publications. These links are maintained by other sources not affiliated with Microsoft Academic Search.
(
www.springerlink.com
)
(
www.springerlink.com
)
(
adsabs.harvard.edu
)
(
www.mis.mpg.de
)
(
arxiv.org
)
More »
Citation Context
(9)
...Connections with antisymmetric torsion on V st 2,4 were investigated in [
1
]...
Ilka Agricola
,
et al.
On the topology and the geometry of SO(3)manifolds
...operator” introduced by B. Kostant ([25], [
1
]) on naturally reductive spaces and with the Dolbeault operator on Hermitian manifolds ([14], [22])...
Ilka Agricola
,
et al.
Eigenvalue estimates for Dirac operators with parallel characteristic ...
...Independently of this development, the past years have shown that nonintegrable geometric structures such as almost hermitian manifolds, contact structures or nonintegrable G2 and Spin(7) structures can be treated successfully with the powerful machinery of metric connections with skewsymmetric torsion (see for example [FrIv02], [
Agr03
], [AgFr04] and the literature cited therein)...
Ilka Agricola
,
et al.
Solvmanifolds with integrable and nonintegrable G 2 structures
...rally reductive space by the help of the subgroup SU(2) ⊂ SL(2, C) (see [
3
], [7])...
Bogdan Alexandrov
,
et al.
Almost Hermitian 6manifolds revisited
...Spaces with parallel torsion are studied in [
1
] in connection with the string model; almost Hermitian 6manifolds with parallel torsion are investigated very recently (after the first version of the present article was posted to the arXiv) in [3]...
Petar Ivanov
,
et al.
SU (3)Instantons and G 2 , Spin (7)Heterotic String Solitons
References
(15)
Parallel spinors and connections with skewsymmetric torsion in string theory
(
Citations: 129
)
Thomas Friedrich
,
Stefan Ivanov
Published in 2001.
Dirac Operator in Riemannian Geometry
(
Citations: 28
)
T. Friedrich
Published in 2000.
Foundations of Differential Geometry I
(
Citations: 66
)
S. Kobayashi
,
K. Nomizu
Published in 1966.
Foundations of Differential Geometry II
(
Citations: 2387
)
S. Kobayashi
,
K. Nomizu
Published in 1969.
Harmonic Spinors on Homogeneous Spaces
(
Citations: 16
)
Gregory D. Landweber
Published in 2000.
Sort by:
Citations
(15)
On the topology and the geometry of SO(3)manifolds
Ilka Agricola
,
Julia BeckerBender
,
Thomas Friedrich
Journal:
Annals of Global Analysis and Geometry  ANN GLOB ANAL GEOM
, vol. 40, no. 1, pp. 6784, 2011
Eigenvalue estimates for Dirac operators with parallel characteristic torsion
(
Citations: 1
)
Ilka Agricola
,
Thomas Friedrich
,
Mario Kassuba
Journal:
Differential Geometry and Its Applications  DIFFERENTIAL GEOM APPL
, vol. 26, no. 6, pp. 613624, 2008
Special Riemannian geometries and the Magic Square of Lie algebras
Jan Gutt
Published in 2008.
Solvmanifolds with integrable and nonintegrable G 2 structures
(
Citations: 6
)
Ilka Agricola
,
Simon G. Chiossi
,
Anna Fino
Journal:
Differential Geometry and Its Applications  DIFFERENTIAL GEOM APPL
, vol. 25, no. 2, pp. 125135, 2007
Almost Hermitian 6manifolds revisited
(
Citations: 20
)
Bogdan Alexandrov
,
Thomas Friedrich
,
Nils Schoemann
Journal:
Journal of Geometry and Physics  J GEOM PHYSICS
, vol. 53, no. 1, pp. 130, 2005