"Vorlesungen über Differentialgeometrie"
E679326
"Vorlesungen über Differentialgeometrie" is a foundational textbook on differential geometry authored by the influential German mathematician Heinz Hopf.
All labels observed (1)
| Label | Occurrences |
|---|---|
| "Vorlesungen über Differentialgeometrie" canonical | 1 |
How this entity was disambiguated
This entity first appeared as the object of triple T7648337 — resolving that mention is where its identity was fixed. The disambiguator weighed these candidate entities and picked the highlighted one (or “None”, minting a new entity). This is how homonymy is resolved: the same surface form can point to different entities.
NED1
Entity disambiguation (via context triple)
gpt-5-mini-2025-08-07
Target entity: "Vorlesungen über Differentialgeometrie" Context triple: [Heinz Hopf, notablePublication, "Vorlesungen über Differentialgeometrie"]
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A.
Vorlesungen über Geometrie
Vorlesungen über Geometrie is a foundational 19th-century textbook on geometry authored by German mathematician Alfred Clebsch.
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B.
Disquisitiones Generales Circa Superficies Curvas
Disquisitiones Generales Circa Superficies Curvas is Carl Friedrich Gauss’s foundational 1827 work on differential geometry, in which he developed the intrinsic theory of curved surfaces and introduced concepts such as Gaussian curvature.
-
C.
Neue Geometrie des Raumes
Neue Geometrie des Raumes is a foundational 19th-century mathematical work by Julius Plücker that develops projective and line geometry in three-dimensional space.
-
D.
Lezioni di calcolo differenziale assoluto
"Lezioni di calcolo differenziale assoluto" is a foundational mathematical text by Tullio Levi-Civita that systematically develops the theory of absolute differential calculus, now known as tensor calculus, with applications to geometry and physics.
-
E.
Geometrical Methods of Mathematical Physics
Geometrical Methods of Mathematical Physics is a widely used textbook that introduces the differential geometric foundations underlying modern theoretical physics, including topics such as manifolds, tensors, and symmetries.
- F. None of above. chosen
- G. Unsure - the case is ambiguous/there is not enough information to decide.
NED2
Entity disambiguation (via description)
gpt-5-mini-2025-08-07
Target entity: "Vorlesungen über Differentialgeometrie" Target entity description: "Vorlesungen über Differentialgeometrie" is a foundational textbook on differential geometry authored by the influential German mathematician Heinz Hopf.
-
A.
Vorlesungen über Geometrie
Vorlesungen über Geometrie is a foundational 19th-century textbook on geometry authored by German mathematician Alfred Clebsch.
-
B.
Disquisitiones Generales Circa Superficies Curvas
Disquisitiones Generales Circa Superficies Curvas is Carl Friedrich Gauss’s foundational 1827 work on differential geometry, in which he developed the intrinsic theory of curved surfaces and introduced concepts such as Gaussian curvature.
-
C.
Neue Geometrie des Raumes
Neue Geometrie des Raumes is a foundational 19th-century mathematical work by Julius Plücker that develops projective and line geometry in three-dimensional space.
-
D.
Lezioni di calcolo differenziale assoluto
"Lezioni di calcolo differenziale assoluto" is a foundational mathematical text by Tullio Levi-Civita that systematically develops the theory of absolute differential calculus, now known as tensor calculus, with applications to geometry and physics.
-
E.
Geometrical Methods of Mathematical Physics
Geometrical Methods of Mathematical Physics is a widely used textbook that introduces the differential geometric foundations underlying modern theoretical physics, including topics such as manifolds, tensors, and symmetries.
- F. None of above. chosen
Statements (25)
| Predicate | Object |
|---|---|
| instanceOf |
book
ⓘ
mathematics textbook ⓘ textbook on differential geometry ⓘ |
| academicDiscipline | geometry ⓘ |
| associatedWithMathematician | Heinz Hopf ⓘ |
| author | Heinz Hopf ⓘ |
| countryOfOrigin | Germany ⓘ |
| field |
differential geometry
ⓘ
mathematics ⓘ |
| hasAuthorNationality | German ⓘ |
| hasInfluenceOn |
modern treatments of differential geometry
ⓘ
research in global differential geometry ⓘ |
| intendedAudience |
advanced mathematics students
ⓘ
research mathematicians ⓘ |
| language | German ⓘ |
| namedAfter | differential geometry ⓘ |
| notableFor |
foundational treatment of differential geometry
ⓘ
influence on 20th‑century differential geometry ⓘ |
| originalTitle | Vorlesungen über Differentialgeometrie ⓘ |
| titleLanguage | German ⓘ |
| topic |
Riemannian geometry
ⓘ
curvature ⓘ curves and surfaces ⓘ geodesics ⓘ topological aspects of differential geometry ⓘ |
How these facts were elicited
The pipeline generated the facts above by prompting gpt-5.1 with this entity's name + description and the instruction below.
Instruction
You are a knowledge base construction expert. Given a subject entity and a description of it, return factual statements that you know for the subject as a JSON list of dictionaries(triples), where keys must be "subject", "predicate" and "object". The number of facts may be very high, between 25 to 50 or more, for very popular subjects. For less popular subjects, the number of facts can be very low, like 5 or 10. # Requirements - If you don't know the subject at all, return an empty list. - If the subject is not a named entity, return an empty list. - Include at least one triple where predicate is "instanceOf". - Do not get too wordy. - Separate several objects into multiple triples with one object.
Input
Subject: "Vorlesungen über Differentialgeometrie" Description of subject: "Vorlesungen über Differentialgeometrie" is a foundational textbook on differential geometry authored by the influential German mathematician Heinz Hopf.
Referenced by (1)
Full triples — surface form annotated when it differs from this entity's canonical label.