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Kentaro Yano (mathematician)

Kentaro Yano (mathematician) is a mathematics topic covered in the lgStudy science library. This page brings together a partial reference excerpt, illustrations, worked examples, real-world applications and a short study plan, so you can understand Kentaro Yano (mathematician) rather than just read about it. In short: Kentaro Yano (1 March 1912 in Tokyo, Japan – 25 December 1993) was a mathematician working on differential geometry who introduced the Bochner–Yano theorem. He also published a classical book about geometric objects (i.e., sections of natural fiber bundles) and Lie derivatives of these objects.

Key takeaways

  • Kentaro Yano (mathematician) belongs to mathematics; place it in that map before memorising details.
  • Learn the definition first, then one example that makes the definition concrete.
  • Connect Kentaro Yano (mathematician) to a quantity you can measure, compute or draw — that is where exam questions come from.
  • Reproduce the core statement of Kentaro Yano (mathematician) from memory before moving on to harder problems.

Reference excerpt

Kentaro Yano (1 March 1912 in Tokyo, Japan – 25 December 1993) was a mathematician working on differential geometry who introduced the Bochner–Yano theorem. He also published a classical book about geometric objects (i.e., sections of natural fiber bundles) and Lie derivatives of these objects.

Publications Les espaces à connexion projective et la géométrie projective des paths, Iasi, 1938 Geometry of Structural Forms (Japanese), 1947 Groups of Transformations in Generalized Spaces, Tokyo, Akademeia Press, 1949 with Salomon Bochner: Curvature and Betti Numbers, Princeton University Press, Annals of Mathematics Studies, 1953 The Theory of Lie Derivatives and its Applications. North-Holland. 1957. ISBN 978-0-7204-2104-0. {{cite book}}: ISBN / Date incompatibility (help) 2020 reprint Differential geometry on complex and almost complex spaces, Macmillan, New York 1965 Integral formulas in Riemannian Geometry, Marcel Dekker, New York 1970 with Shigeru Ishihara: Tangent and cotangent bundles: differential geometry, New York, M. Dekker 1973 with Masahiro Kon: Anti-invariant submanifolds, Marcel Dekker, New York 1976 Morio Obata (ed.): Selected papers of Kentaro Yano, North Holland 1982 with Masahiro Kon: CR Submanifolds of Kählerian and Sasakian Manifolds, Birkhäuser 1983 2012 reprint with Masahiro Kon: Structures on Manifolds, World Scientific 1984

References

External links Kentaro Yano at the Mathematics Genealogy Project O'Connor, John J.; Robertson, Edmund F., "Kentaro Yano", MacTutor History of Mathematics Archive, University of St Andrews

Worked examples

Example 1 — a first encounter with Kentaro Yano (mathematician)

Start with the simplest possible case. Write down what Kentaro Yano (mathematician) claims or describes in one sentence, then invent the smallest concrete situation in which that sentence is true. In mathematics, the smallest case is usually a single object, a single equation or a single measurement. Check that every symbol or term in your sentence has a meaning in that case.

Example 2 — changing one variable

Take the situation from Example 1 and change exactly one quantity: double it, halve it, or set it to zero. Predict what should happen to Kentaro Yano (mathematician) before you calculate. Comparing your prediction with the result is the fastest way to find out whether you understand the idea or only the words.

Example 3 — an exam-style question

Typical questions about Kentaro Yano (mathematician) ask you to (a) state it precisely, (b) apply it to given data, and (c) explain a limitation. Practise writing all three answers in under five minutes; the third part is what separates a full-mark answer from an average one.

Applications of Kentaro Yano (mathematician)

In research
Kentaro Yano (mathematician) appears in mathematics research whenever the underlying quantities have to be modelled precisely. Papers usually cite it as a starting assumption and then explore where it breaks down.
In technology and industry
Engineering practice reuses Kentaro Yano (mathematician) in design rules, simulations and safety margins. Knowing the idea lets you read a specification sheet and understand why the numbers look the way they do.
In the classroom
Kentaro Yano (mathematician) is common in secondary-school and first-year university syllabi. It links to neighbouring topics 1912 births, 1993 deaths, 20th-century Japanese mathematicians, so understanding it makes those chapters shorter.
In everyday life
Look for Kentaro Yano (mathematician) outside the textbook — in sport, cooking, traffic, electronics or the sky above you. An example you found yourself is remembered far longer than one you were given.
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How to study Kentaro Yano (mathematician) in 20 minutes

  1. Read the reference excerpt below once, without taking notes.
  2. Close the page and write down what Kentaro Yano (mathematician) means in your own words.
  3. Compare your version with the excerpt and mark what you missed.
  4. Work through the three examples above with pen and paper.
  5. Explain Kentaro Yano (mathematician) out loud to somebody else — or to Teacher Smith in the lgStudy chat.

Frequently asked questions

What is Kentaro Yano (mathematician) in simple terms?

Kentaro Yano (1 March 1912 in Tokyo, Japan – 25 December 1993) was a mathematician working on differential geometry who introduced the Bochner–Yano theorem. He also published a classical book about geometric objects (i.e., sections of natural fiber bundles) and Lie derivatives of these objects.

Why does Kentaro Yano (mathematician) matter?

Because it connects several mathematics ideas at once: it gives you a definition you can apply, a quantity you can calculate, and a way to check whether a result is plausible.

How should I study Kentaro Yano (mathematician)?

Read the excerpt, restate it from memory, then work through the examples and applications listed on this page. The five-step study plan above takes about twenty minutes.

What does this page cover?

It gives you a compact reference excerpt plus original lgStudy explanations, examples, applications and study material on Kentaro Yano (mathematician).

Tags

  • 1912 births
  • 1993 deaths
  • 20th-century Japanese mathematicians
  • Differential geometers

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