Research on the singularities and the event horizon in the brane world model

• Project/Area Number: 21654007
• Research Category: Grant-in-Aid for Challenging Exploratory Research
• Allocation Type: Single-year Grants
• Research Field: Geometry
• Research Institution: Hokkaido University
• Principal Investigator: IZUMIYA Shyuichi 北海道大学, 大学院・理学研究院, 教授 (80127422)
• Project Period (FY): 2009 – 2011
• Project Status: Completed (Fiscal Year 2011)
• Budget Amount: ¥3,300,000 (Direct Cost: ¥3,000,000、Indirect Cost: ¥300,000); Fiscal Year 2011: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000); Fiscal Year 2010: ¥1,000,000 (Direct Cost: ¥1,000,000); Fiscal Year 2009: ¥1,000,000 (Direct Cost: ¥1,000,000)
• Keywords: ブレーン / 特異点論 / 焦面 / 事象の地平線 / ブラックホール / ブレーン宇宙論 / 反ド・ジッター空間 / ミンコフスキー空間 / 世界膜 / 光的タイト部分多様体 / 限界捕捉面 / ブレーンワールド / ミンコフスキー時空 / 極小曲面 / 極大曲面 / 平均曲率一定

Research Abstract

We have progressed the research on local and global properties of geometric invariants for spacelike submanifolds in anti de Sitter space-time and Minkowski space-time. As a consequence, we have introduced the notion of lightlike tightness for spacelike submanifolds. We have also determined the partial differential equations for Marginally trapped sufaces of graph type in Minkowski space-time.

Research Products

• [Journal Article] Extensions of the mandala of Legendrian, dualities for pseudo-spheres in Lorentz Minkowski space (2012)
  • Author(s): Shyuichi Izumiya and Handan Yildirim
  • Journal Title: Topology and its Applications Volume: 159(2) Issue: 2 Pages: 509-518
  • DOI: 10.1016/j.topol.2011.09.026
  • Peer Reviewed
• [Journal Article] On caustics of submanifolds and canal hypersurfaces in Euclidean space (2012)
  • Author(s): Shyuichi Iziumiya and Masatomo Takahash
  • Journal Title: Topology and its Applications Volume: 159(2) Issue: 2 Pages: 509-518
  • DOI: 10.1016/j.topol.2011.09.025
  • Peer Reviewed
• [Journal Article] Marcelo Buosis and Maria Aparecida Soares Ruas, Horo-tight spheres in hyprbolic space (2011)
  • Author(s): Shyuichi Izumiya
  • Journal Title: Geometriae Dedicata Volume: 154(1) Issue: 1 Pages: 9-26
  • DOI: 10.1007/s10711-010-9565-9
  • Peer Reviewed
• [Journal Article] Slant geometry of spacelike hypersurfaces in the lightcone (2011)
  • Author(s): Shyuichi Izumiya and Handan Yildirim
  • Journal Title: Journal of the Mathematical Society of Japan Volume: 63 Issue: 3 Pages: 715-752
  • DOI: 10.2969/jmsj/06330715
  • NAID: 10029321803
  • ISSN: 0025-5645, 1881-1167, 1881-2333
  • Peer Reviewed
• [Journal Article] Great circular surfaces in the three-sphere (2011)
  • Author(s): Shyuichi Izumiya, Takayuki Nagai and Kentaro Saji
  • Journal Title: Differential Geometry and its Applications Volume: 29 Issue: 3 Pages: 409-425
  • DOI: 10.1016/j.difgeo.2011.02.005
  • Peer Reviewed
• [Journal Article] The mandala of Legendrian dualities for pseudo-spheres in Lorentz-Minkowski space and "flat" spacelike surfaces (2010)
  • Author(s): Shyuichi Izumiya and Kentaro Saji
  • Journal Title: Journal of Singularities Volume: 2 Pages: 92-127
  • DOI: 10.5427/jsing.2010.2g
  • Peer Reviewed
• [Journal Article] Total absolute horospherical curvature of submanifolds in hyperbolic space (2010)
  • Author(s): Marcelo Buosi, Shyuichi Izumiya and Maria Aparecida Soares Ruas
  • Journal Title: Advanes in Geometry Volume: 10(4) Issue: 4 Pages: 603-620
  • DOI: 10.1515/advgeom.2010.029
  • Peer Reviewed
• [Journal Article] Folding maps on spacelike and timelike surfaces and duality (2010)
  • Author(s): S. Izumiya, M. Takahashi and F. Tari
  • Journal Title: Osaka Journal of Mathematics Volume: 47 Pages: 839-862
  • Peer Reviewed
• [Journal Article] Horospherical flat surfaces in Hyperbolic 3-space (2010)
  • Author(s): S. Izumiya, K. Saji and M. Takahashi
  • Journal Title: Journal of the Mathematical Society of Japan Volume: 62 Issue: 3 Pages: 789-849
  • DOI: 10.2969/jmsj/06230789
  • NAID: 10027870826
  • ISSN: 0025-5645, 1881-1167, 1881-2333
  • Peer Reviewed
• [Journal Article] Self-adjoint operators on surfaces with singular metrics (2010)
  • Author(s): S. Izumiya and F. Tari
  • Journal Title: Journal of Dynamical and Control Systems Volume: 16(3) Issue: 3 Pages: 329-353
  • DOI: 10.1007/s10883-010-9096-6
  • Peer Reviewed
• [Journal Article] Singularities of Anti de Sitter torus Gauss maps (2010)
  • Author(s): Liang Chen and Shyuichi Izumiya
  • Journal Title: Bulletin of Brazilian Mathematical Society Volume: 41(1) Pages: 37-61
  • URL: http://www.springerlink.com/content/e617n7x3k947w175/
  • Peer Reviewed
• [Journal Article] Juan Jose Nuno Ballesteros and Maria del Carmen Romero Fuster, Global properties of codimension two spacelike submanifods in Minkowski space (2010)
  • Author(s): Shyuichi Izumiya
  • Journal Title: Advances in Geometry Volume: 10 Pages: 51-75
  • Peer Reviewed
• [Journal Article] Projections of surfaces in the hyperbolic space along horocycles (2010)
  • Author(s): Shyuichi Izumiya and Farid Tari
  • Journal Title: Proceedings of the Royal Society of Edinburgh Volume: 140A Pages: 399-418
  • Peer Reviewed
• [Journal Article] Lightlike developables in Minkowski 3-space (2010)
  • Author(s): Sachiko Chino and Shyuichi Izumiya
  • Journal Title: Lightlike developables in Minkowski Demonstratio Mathematica Volume: XLIII(2) Pages: 387-399
  • URL: http://www.ams.org/distribution/mmj/vol9-2-2009/cont9-2-2009.html
  • Peer Reviewed
• [Journal Article] Total absolute horospherical curvature of submanifolds in hyperbolic space (2010)
  • Author(s): Shyuichi Izumiya
  • Journal Title: Advanes in Geometry Volume: 10 Pages: 602-620
  • Peer Reviewed
• [Journal Article] Folding maps on spacelike and timelike surfaces, duality (2010)
  • Author(s): Shyuichi Izumiya
  • Journal Title: Osaka Journal of Mathematics Volume: 47 Pages: 829-862
  • Peer Reviewed
• [Journal Article] The mandala of Legendrian dualities for pseudo-spheres in Lorentz-Min kowski space, "flat" spacelike surfaces (2010)
  • Author(s): Shyuichi Izumiya
  • Journal Title: Journal of Singularities Volume: 2 Pages: 92-127
  • Peer Reviewed
• [Journal Article] Legendrian dualities and spacelike hypersurfaces in the lightcone (2009)
  • Author(s): Shyuichi Izumiya
  • Journal Title: Moscow Mathematical Journal Volume: 9(2) Pages: 325-357
  • URL: http://www.ams.org/distribution/mmj/vol9-2-2009/cont9-2-2009.html
  • Peer Reviewed
• [Journal Article] Spacelike surfaces in Anti de Sitter Four-Space from a Contact Viewpoint (2009)
  • Author(s): Shyuichi Izumiya, Donghe Pei and Maria del Carmen Romero Fuster
  • Journal Title: Proceedings of the Steklov Institute of Mathematics Volume: 267 Issue: 1 Pages: 156-173
  • DOI: 10.1134/s0081543809040130
  • Peer Reviewed
• [Journal Article] Flat lightlike hypersurfaces in Lorentz-Minkowski 4-space (2009)
  • Author(s): Shyuichi Izumiya, Maria del Carmen Romero Fuster and Kentaro Saji
  • Journal Title: Journal of Geometry and Physics Volume: 59 Pages: 1528-1546
  • Peer Reviewed
• [Journal Article] Horospherical geometry in the hyperbolic space (2009)
  • Author(s): Shyuichi Izumiya
  • Journal Title: Advanced Studies in Pure Mathematics Volume: 55 Pages: 31-49
  • Peer Reviewed
• [Journal Article] Flat lightlike hypersurfaces in Lorentz-Minkowski 4-space (2009)
  • Author(s): S.Izumiya
  • Journal Title: Journal of Geometry and Physics 59 Pages: 1528-1546
  • Peer Reviewed
• [Journal Article] Legendrian dualities and spacelike hypersurfaces in the lightcone (2009)
  • Author(s): S.Izumiya
  • Journal Title: Moscow Mathematical Journal 9 Pages: 325-357
  • Peer Reviewed
• [Journal Article] Spacelike surfaces in Anti de Sitter Four-space from a contact viewpoint (2009)
  • Author(s): S.Izumiya
  • Journal Title: Proceedings of the Steklov Institute of Mathematics 267 Pages: 156-173
  • Peer Reviewed
• [Presentation] ミンコフスキー時空内の限界捕捉面、特異点論とその応用 (2011)
  • Author(s): 泉屋周一
  • Place of Presentation: 大分高専
  • Year and Date: 2011-06-02
• [Presentation] ミンコフスキー空間内の限界捕捉面 (2011)
  • Author(s): 泉屋周一
  • Organizer: 特異点論とその応用
  • Place of Presentation: 大分工業高専(大分市)(招待講演)
  • Year and Date: 2011-06-02
• [Presentation] The lightlike geometry of spacelike submanifolds in Lorentz-Minkowski space (2011)
  • Author(s): Shyuichi Izumiya
  • Organizer: Differential Geometry and Tanaka Theory
  • Place of Presentation: 京都大学京都大学
  • Year and Date: 2011-01-26
• [Presentation] Singularities of Gauss maps; revisited (2010)
  • Author(s): Shyuichi Izumiya
  • Organizer: 11th International Workshop on Real and Complex Singularities
  • Place of Presentation: Sao Paulo大学(Brazi、Sao Carlos) 招待講演
  • Year and Date: 2010-07-30
• [Presentation] Singularities of Gauss maps (2010)
  • Author(s): Shyuichi Izumiya
  • Organizer: 11th International Workshop on Real and Complex Singularities
  • Place of Presentation: Sao Paulo University
  • Year and Date: 2010-07-03
• [Presentation] Singularities of caustics emitted by timelike hypersurfaces in Anti de Sitter space (2009)
  • Author(s): Shyuichi Izumiya
  • Organizer: JSPS forum Singularities and Applications, Strasbourg
  • Place of Presentation: Strasbourg University
  • Year and Date: 2009-08-25
• [Presentation] Caustic emanating from hyperbranes in Anti de Sitter space (2009)
  • Author(s): 泉屋周一
  • Organizer: CNRS-JSPS日仏数学シンポジウム
  • Place of Presentation: Strasburg大学、仏国
  • Year and Date: 2009-08-24
• [Presentation] Differential Geometry from the view point of Singularity Theory (2009)
  • Author(s): S. Izumiya and M. Ruas
  • Organizer: 1st Workshop on Singularities in Generic Geometry and Applications
  • Place of Presentation: Valencia University
• [Remarks]
  • URL: http://researchmap.jp/izumiya/
• [Remarks]
  • URL: http://researchmap.jp/izumiya/
• [Remarks]
  • URL: http://researchmap.jp/izumiya/