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In mathematics the technical term Riemann manifold (or Riemannian manifold) denotes a type of space investigated by the nineteenth century German mathematician Bernhard Riemann.
The corresponding Russian term is sometimes written римановое многообразие: no surprise here. However I seem to have more often come across the expression риманово (without an е at the end) многообразие.
Since the genitive of Pиман is, I guess, Pимана with upper case P, the shorter (and to me stranger) form риманово cannnot be a genitive and seems thus also to be an adjective.
What is the explanation for this variant ?

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    Риманово многообразие/ риманово пространство/ гилбертово пространство/ евклидово пространство/ пространство Лобачевского
    – Elena
    Mar 29 '19 at 9:20
  • Thank you for the interesting examples, Elena. Mar 29 '19 at 9:45
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These are so-called possessive adjectives which are used extensively (but not exclusively) in science, medicine and religion:

  • булева алгебра
  • базедова болезнь
  • ахиллесова пята
  • прокрустово ложе
  • декартово произведение
  • сизифов труд

They are formed by adding the suffix -ов (-ев, -ёв) to the motivating stem (usually denoting a person). Russian surnames (Иванов, Петров) have the same structure and follow the same declension pattern, except for the prepositional case: об ивановом - об Иванове.

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  • @Georges Elencwajg in the modern language -ов surnames aren't perceived as possessive adjectives and are inflected as nouns instead which is morphologically manifest in Prepositional case and also in Dative ивановому (adj) vs Иванову (noun), but paradigmatically in all cases in the form of accent shift, Nom. ивАнов (adj.) vs ИванОв (noun), Gen & Acc. ивАнова (adj) vs ИванОва (noun), Inst. ивАновым (adj) vs ИванОвым (noun) Mar 29 '19 at 10:01
  • @ Баян Купи-ка: Yes, but here the name is Риман, not Риманов, so it seems to me that we can only be faced with an adjective. Mar 29 '19 at 10:06
  • @Sergey: but if we have a possessive adjective, I don't understand why it is not in the neutral form римановоe многообразие, just as in your example булева алгебра. Are there adjectives in the neutral gender that end with -o? I thought that -o ending was for neutral nouns, not adjectives. Mar 29 '19 at 10:12
  • @Georges Elencwajg indeed, in the phrase you're asking about it IS possessive adjective, i've only explained the difference Sergey mentioned... possessive adjectives only have a form which corresponds to the shortened form of standard adjective so while the short neuter form of хорошее is хорошо there's only one possessive adjective form риманово, there's no such adjective as римановый/-ая/-ое and it wouldn't make much sense from the semantic perspective as it would have the connotation of made of Риман or having the qualities of Риман Mar 29 '19 at 11:07
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    @Georges Elencwajg a good example of the difference can be made with the adjective урановый - there's a chemical element уран and there's a Greek god Уран (whom the element is named after), the adjective урановый/-ая/-ое always refers to уран the element - урановый рудник, урановая бомба, урановое стекло that is related to Uranium or made of Uranium, however with reference to Уран the god the only correct adjective would be possessive Уранов because it's an animate noun describing an individual able to possess things unlike уран the element Mar 29 '19 at 12:39
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This is a possessive adjectival form.

Притяжательные прилагательные - разряд прилагательных, выражающих принадлежность чего-либо лицу или животному (отцовы сапоги, волчья нора). П. п. образуются с помощью суффиксов -ов(-ев), -ин, -ий.

source

The suffix -ов(-ев) doesn't seem to be productive any longer so its use is confined to proper names and members of stable collocations which emerged when it was still current. To name a few базедова болезнь (after physician Basedow), прокрустово ложе (after mythological figure Procrustes), Эйфелева башня (after Gustave Eiffel), бикфордов шнур (after William Bickford), бертоллетова соль (after Сlaude Berthollet), крокодиловы слёзы (today we'd say крокодильи).

This is the same form as the one typical Russian surnames are fashioned in (Иванов ← Иван, Петров ← Пётр, Сидоров ← Сидор). Originally it was supposed to be followed by the words сын or дочь and functioned as patronymic before formal surnames appeared → Марья Иванова дочь, Фёдор Петров сын, much like is the case of many Anglo-Saxon, Scandinavian and other nations' surnames. In Russian it may look unusual in neuter gender, because we're used to it in either masculine or feminine.

It's also employed in the expression драть как Cидорову козу where Cидорова means Sidor's (feminine).

Possessive adjectives answer the question чей? (whose?) whereas regular adjectives answer the question какой? (what (kind of)? which?)

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    I'd like to add that римановое sounds really awkward to me (russian native). About as awkward as "Пифагоровые штаны"...
    – tum_
    Mar 29 '19 at 5:20
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    As a variation of the possessive, "римановское" is grammatically possible here. The choice depends on tradition (броуновское движение vs броуново, эйнштейновская теория vs эйнштейнова).
    – Alex_ander
    Mar 29 '19 at 6:14
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    @tum_: I have no idea what you mean by "Пифагоровые штаны", since штаны seems to mean trousers. Are you being sarcastic? Anyway that an expression "sounds really awkward to a Russian native" does not explain to a non-native speaker what he should use. Mar 29 '19 at 10:32
  • It's also employed in the expression драть как Cидорову козу where Cидорова means - LOL! "demanding scrupulous adhering to mutually exclusive paragraphs". Here they make "Sidorova" a clear female surname. Because a possessive "Sidor's" would be written with small "c" like all the examples before.
    – Arioch
    Mar 29 '19 at 13:58
  • @GeorgesElencwajg "пифагоровы штаны во все стороны равны" - that is a humorous saying, albeit I can hardly grasp its sense too. The graphical representations of the theorem might be seen as some quite strange sort of pants form some uber-simplistic cartoons. Guess it helped students to remember this theorem is somehow about triangles and squares
    – Arioch
    Mar 29 '19 at 14:04
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Римановое is plain wrong - it turns animate subject into inanimate adjective.

However, Римановское exists as a variant of norm, that is of Риманово.

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