If what N2 refers to in the noun phrase "N1のN2" is known to the participants of the conversation, N2 can be omitted. Typically, の has a possessive meaning. When N2 is a person, it cannot be omitted.
Mr./Ms. Tanaka is my teacher.
その じてんしゃは だれの じてんしゃですか。
Whose bicycle is that bicycle?
→その じてんしゃは だれのですか。
Whose is that bicycle?
この じてんしゃは わたしの じてんしゃです。
This bicycle is my bicycle.
→この じてんしゃは わたしのです。
This bicycle is mine.
これは マナさんのでは ありません。
This is not Mana's.