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Abu Dhabi: Jan 4, 2014
The 31-year-old paceman was not played in the first Test against Pakistan which ended in a draw on the fifth and final day on Saturday.
“Kulasekara suffered a hamstring injury which was discovered recently and will be returning home,” said Mathews.
There will be no replacement for Kulasekara as Sri Lanka have enough fast bowlers in the squad, said Mathews.
Pakistan had suffered two blows with paceman Umar Gul released from the squad after not recovering fully from a knee operation and wicketkeeper Adnan Akmal also returned home after fracturing his finger during the first Test.
Kulasekara has so far played 20 Tests, 146 one-days and 32 Twenty20s for Sri Lanka.
Sri Lanka have pacemen Suranga Lakmal, Shaminda Eranga, Nuwan Pradeep and uncapped Vishwa Fernando in their squad.
The second of three Tests starts in Dubai on Wednesday.
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