||श्री कृष्णः शरणं मम||
||श्री कृष्णं शरणं मम||
||श्री कृष्णाय शरणं मम||
||श्री कृष्ण शरणं मम||
I see all these various forms online. Which one is correct grammatically?
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Note that this question would be more suitable for Sanskrit Language site which is currently in definition phase.
There are 7 cases of Nouns called Vibhakti (विभक्ति). (Quoting useful information regarding this from one Sanskrit Grammar tutorial site:
The following are the 7 different cases of a noun.
- Case 1 - Nominative -> प्रथमा / prathamaa
- Case 2 - Accusative -> द्वितीया / dvitiiyaa
- Case 3 - Instrumental -> तृतीया / tRRitiiya
- Case 4 - Dative -> चतुर्थी / chaturthii
- Case 5 - Ablative -> पञचमी / paJNamii
- Case 6 - Genitive -> षष्ठी / ShaShThii
- Case 7 - Locative -> सप्तमी / saptamii
- Vocative -> सम्बोधन / sambodhana
श्री कृष्णः शरणं मम। means "Lord Krishna is my refuge" or "Shri Krishna is my shelter." (As already explained by Jonathan in the answer). Here Krishna is the subject/nominative in the sentence. Now let's see an example for the various forms of Sanskrit according to the case of Noun mentioned above:
(Here I'm quoting the forms of Sanskrit based on 7 cases of noun in tabular form for a boy बाल):
You may also refer Wikipedia page on Sanskrit Grammar which provides forms fro Rama (राम).
So, the grammatically correct Saranagati Mantra is:
॥श्री कृष्णः शरणं मम॥
श्री कृष्णः = Shri KRshNa: (subject case).
मम = mine (possessive case)
शरणं = protection/refuge (object case)
शरणं मम = my refuge.
So this roughly translates KRshna: is my refuge. Since this is in Sholka "अस्ति" is omitted.
Ideally, if prose, it would read "श्री कृष्णः मम शरणं अस्ति |"