| Project/Area Number |
19540066
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Single-year Grants |
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| Section | 一般 |
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| Research Field |
Geometry
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| Research Institution | Chiba University |
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Principal Investigator |
INABA Takashi Chiba University, 大学院・理学研究科, 教授 (40125901)
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| Co-Investigator(Kenkyū-buntansha) |
TSUBOI Takashi 東京大学, 大学院・数理科学研究科, 教授 (40114566)
NAKAYAMA Hiromichi 青山学院大学, 理工学部, 教授 (30227970)
KUGA Kenichi 千葉大学, 大学院・理学研究科, 教授 (30186374)
SUGIYAMA Ken-ichi 千葉大学, 大学院・理学研究科, 教授 (90206441)
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| Project Period (FY) |
2007 – 2009
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| Project Status |
Completed (Fiscal Year 2009)
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| Budget Amount *help |
¥3,120,000 (Direct Cost: ¥2,400,000、Indirect Cost: ¥720,000)
Fiscal Year 2009: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2008: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2007: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
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| Keywords | 微分トポロジー / 積分不可能平面場 / エントロピー / 接触構造 / エンゲル構造 / 積分曲線 |
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| Research Abstract |
In this research we investigated non-integrable tangent distributions on manifolds from the global viewpoint. In particular, we took up the notion of entropy and examined its significance in measuring the complexity of such distributions. The notion of entropy for non-integrable distributions was first introduced by Bis in 2005. We gave a somewhat different definition from his one, and proved the vanishing of the entropy for non-affine Engel distributions on 4-dimensional manifolds.
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