Compact Manifolds with Special Holonomy

By D. Joyce. 2000

1,242 citations recorded by the source corpus.

View Paper: https://www.semanticscholar.org/paper/0e485a2dcb87f92fbdb801a4b8a521abe1cd4ddc

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1. M. Graña
2. Thomas W. Grimm
3. D. Lust
4. J. Gauntlett
5. Paul Koerber
6. Ralph Blumenhagen
7. E. Witten
8. D. Martelli

Citations in the corpus

• An introduction to potential theory in calibrated geometry (2007, background): “For the general construction of such spaces with SU(n), Sp(n), G2, or Spin7 holonomy, the reader is referred to the book of Joyce [J].”
• New aspects of the ddc-lemma (2005, unknown): “is an isomorphism [47].”
• Dirichlet Branes and Mirror Symmetry (2009, background): “The metric can be expressed in terms of a Kähler potential depending only on ∑ |zi|(2) [274].”
• Superstrings with intrinsic torsion (2003, background): “It is the opposite to the conventions given, for instance in [52].”
• Notes on the octonions (2010, methodology): “Every spin 7–manifold admits a G2–structure [Lawson1989]; concrete examples are S7 (considered as unit sphere in the octonions), S1 × Z where Z is a Calabi–Yau 3–fold and various resolutions of T7/Γ where Γ is an appropriate finite group, see [19].”
• Some Notes on G_2 and Spin(7) Geometry (2006, background): “These notes are purely expository and are made available as a potentially useful resource to others.”
• G2-instantons on generalised Kummer constructions (2011, unknown): “For a more comprehensive treatment we refer the reader to Joyce’s book [18], specifically Chapter 10.”
• Ricci-flat Kähler metrics on crepant resolutions of Kähler cones (2008, background): “But in this case there is an improved proof, by Joyce [22,23], which proves Theorem 1.”
• Dynamical stability and instability of Ricci-flat metrics (2013, background): “Ricci-flat metrics are fairly hard to construct, and their properties are of great interest, see [1, 8, 9] for extensive information.”
• Flux compactifications in string theory: A Comprehensive review (2005, background): “, a connection satisfying ∇mgnp = 0), possibly with torsion6, which is also compatible with the structure and such that ∇mη = 0 [71].”
• A new construction of compact torsion-free $G_2$-manifolds by gluing families of Eguchi–Hanson spaces (2017, methodology): “7 in [20] implies that (φ̃t , g̃ N t ) depends smoothly on t ∈ (0, ǫ], as (φt , g t ) does.”
• Kähler Reduction of Metrics with Holonomy G2 (2003, background): “This theory is elaborated in the standard references [13, 19, 25, 29] We denote by (N, ǩ) the Riemannian quotient of (Y, k), so that N is a 6dimensional manifold formed from the orbits of the Killing vector field V .”
• Low-dimensional homogeneous Einstein manifolds (2005, background): “However, there are results for many interesting classes of Einstein metrics, such as K¨ ahler-Einstein metrics [Yau], [Tia], metrics with small holonomy group [ Jo ], Sasakian-Einstein metrics [BoGa] and homogeneous Einstein metrics [He], [BWZ] (cf.”