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  1. Consequently, they go by slightly different names, depending mostly on context, such as Calabi-Yau manifolds or Calabi-Yau varieties.[1]
  2. A Calabi-Yau space is characterized by the existence of a nonvanishing harmonic spinor .[1]
  3. On a Calabi-Yau manifold , such a can be defined globally, and the Lie group is very important in the theory.[1]
  4. In fact, one of the many equivalent definitions, coming from Riemannian geometry, says that a Calabi-Yau manifold is a -dimensional manifold whose holonomy group reduces to .[1]
  5. Unfortunately, there are tens of thousands of possible Calabi-Yau manifolds for six dimensions, and string theory offers no reasonable means of determining which is the right one.[2]
  6. Calabi-Yau manifolds have become a topic of study in both mathematics and physics, dissolving the boundaries between the two subjects.[3]
  7. Calabi-Yau manifolds are complex manifolds, that is, they can be disassembled into patches which look like flat complex space.[3]
  8. Proving a conjecture of Eugenio Calabi, Shing-Tung Yau has shown that Calabi-Yau manifolds have a property which is very interesting to physics.[3]
  9. By Yau's theorem, not only is flat space a solution but so are Calabi-Yau manifolds.[3]
  10. Particularly in superstring theory, the extra dimensions of spacetime are sometimes conjectured to take the form of a 6-dimensional Calabi–Yau manifold, which led to the idea of mirror symmetry.[4]
  11. On the other hand, their double covers are Calabi–Yau manifolds for both definitions (in fact, K3 surfaces).[4]
  12. Most definitions assert that Calabi–Yau manifolds are compact, but some allow them to be non-compact.[4]
  13. Some definitions put restrictions on the fundamental group of a Calabi–Yau manifold, such as demanding that it be finite or trivial.[4]
  14. By the conjecture of Calabi (1957) proved by Yau (1977; 1979), there exists on every Calabi-Yau manifold a Kähler metric with vanishing Ricci curvature.[5]
  15. While many beautiful properties of Calabi-Yau manifolds have been discovered, more questions have been raised and probed.[5]
  16. This proves the existence and provides a criterion for Kähler Calabi-Yau manifolds.[5]
  17. By convention, Calabi-Yau manifolds exclude those with infinite fundamental groups.[5]
  18. This is where all the interest into these Calabi-Yau manifolds in string theory comes from.[6]
  19. One also speaks of generalized Calabi-Yau spaces.[6]
  20. This is reflected notably in the mirror symmetry of the target Calabi-Yau manifolds.[6]
  21. For more see Calabi-Yau manifolds in SU-bordism theory.[7]
  22. Abstract We study aspects of the geometry and physics of type II string theory compactification on Calabi-Yau manifolds.[8]
  23. The emphasis is on non-perturbative phenomena which arise when the compactification manifold develops singularities, and the implications on quantum geometry of the the Calabi-Yau spaces.[8]
  24. If not, check out this Calabi-Yau manifold by the artist Bathsheba.[9]
  25. Abstract We study the existence of special Lagrangian submanifolds of log Calabi–Yau manifolds equipped with the complete Ricci-flat Kähler metric constructed by Tian and Yau.[10]
  26. We prove that if X is a Tian–Yau manifold and if the compact Calabi–Yau manifold at infinity admits a single special Lagrangian, then X admits infinitely many disjoint special Lagrangians.[10]
  27. Surveys in Dierential Geometry XIII A survey of Calabi-Yau manifolds Shing-Tung Yau Contents Introduction 1. 2.[11]
  28. The Ricci tensor of Calabi-Yau manifolds 2.2.[11]
  29. Examples of compact Calabi-Yau manifolds 2.6.[11]
  30. Noncompact Calabi-Yau manifolds 2.7.[11]
  31. Their size and six dimensions make Calabi-Yau spaces difficult to draw.[12]
  32. Calabi-Yau manifolds are complex geometrical spaces studied in mathematics and physics.[13]
  33. Different Calabi-Yau manifolds described by different quantum theories turn out to encode the same physics.[13]
  34. These shapes are known as Calabi-Yau manifolds — an example of which is depicted in this demonstration.[14]
  35. One of the main motivations for studying the collapsing of Ricci-flat Calabi-Yau manifolds comes from mirror symmetry.[15]
  36. A review of the necessary mathematics is undertaken fol- lowed by a review of the Calabi-Yau manifold and its role in physics.[16]
  37. The complete intersection Calabi-Yau manifold is explained and a machine learning approach is motivated.[16]
  38. Neural networks are then employed to learn the Hodge numbers of complex dimension 4 complete intersection Calabi-Yau manifolds.[16]
  39. In order for it to also produce a supersymmetric gauge theory with a realistic particle spectrum, the 6-manifold must be a Calabi-Yau manifold.[16]
  40. Calabi-Yau manifolds play an important role in physics owing to the part they play in passing from a 10-dimensional string theory vacuum to the observed world of four dimensions.[17]
  41. This speaker will comment on the mysterious modular behaviour of the zeta-function for the case that the Calabi-Yau manifold is singular.[17]
  42. We rst briey mention some of the work in Kahler Calabi-Yau manifolds that was inuenced by the discovery of mirror symmetry in the late 1980s.[18]
  43. We then discuss some of the mathemat- ical motivations behind the recent work on non-Kahler Calabi-Yau manifolds, which arise in string compactications with uxes.[18]
  44. After extending mirror symmetry to non-Kahler Calabi-Yau manifolds, we show how this leads to new cohomologies and invariants of non-Kahler symplectic manifolds.[18]
  45. As a prime example, mathematical research on Calabi-Yau spaces over the past two decades has been strongly motivated by string theory, and in particular, mirror symmetry.[18]
  46. Maximal automorphisms of Calabi-Yau manifolds versus maximally unipotent monodromy.[19]
  47. In the case that the group action has fixed points, it is often possible to resolve the resulting orbifold singularities in such a way as to again obtain a Calabi-Yau manifold.[20]
  48. Topologically, such a process is a surgery and yields a Calabi-Yau manifold topologically distinct from the original.[20]
  49. Only a little more difficult is the converse: under what conditions is a Calabi-Yau manifold, given that is?[20]
  50. In even dimensions, on the other hand, this simple calculation shows that there are no multiply-connected Calabi-Yau manifolds.[20]
  51. Calabi-Yau spaces are complex spaces with a vanishing first Chern class, or equivalently, with trivial canonical bundle (canonical class).[21]

소스

  1. ↑ 1.0 1.1 1.2 1.3 Calabi-Yau Space -- from Wolfram MathWorld
  2. ↑ String Theory and Calabi-Yau Manifolds
  3. ↑ 3.0 3.1 3.2 3.3 C is for Calabi-Yau Manifolds
  4. ↑ 4.0 4.1 4.2 4.3 Calabi–Yau manifold
  5. ↑ 5.0 5.1 5.2 5.3 Calabi-Yau manifold
  6. ↑ 6.0 6.1 6.2 supersymmetry and Calabi-Yau manifolds in nLab
  7. ↑ Calabi-Yau variety in nLab
  8. ↑ 8.0 8.1 String Theory on Calabi-Yau Manifolds: Topics in Geometry and Physics
  9. ↑ Visualizing Calabi-Yau Manifolds
  10. ↑ 10.0 10.1 Special Lagrangian submanifolds of log Calabi–Yau manifolds
  11. ↑ 11.0 11.1 11.2 11.3 Surveys in differential geometry xiii
  12. ↑ Calabi-Yau Manifold Crystal
  13. ↑ 13.0 13.1 On the Homepage: A Calabi-Yau Manifold
  14. ↑ 4.3 Gravity Calabi-Yau Manifold
  15. ↑ Collapsing Calabi-Yau Manifolds: August 31 – September 4, 2015
  16. ↑ 16.0 16.1 16.2 16.3 Machine learning
  17. ↑ 17.0 17.1 Geometry and Arithmetic of Calabi-Yau Manifolds
  18. ↑ 18.0 18.1 18.2 18.3 Proceedings of symposia in pure mathematics
  19. ↑ Higher-Dimensional Modular Calabi–Yau Manifolds
  20. ↑ 20.0 20.1 20.2 20.3 The Expanding Zoo of Calabi-Yau Threefolds
  21. ↑ Calabi-Yau Manifolds
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